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A note on m-factorizations of complete multigraphs arising from designs

György Kiss, Christian Rubio-Montiel
<span title="2014-09-28">2014</span> <i title="University of Primorska Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gvgtrk4iyvatbibvfwr3uifrji" style="color: black;">Ars Mathematica Contemporanea</a> </i> &nbsp;
Some new infinite families of simple, indecomposable m-factorizations of the complete multigraph λ K_v are presented. Most of the constructions come from finite geometries.  ...  Most of these constructions arise from finite geometry. The aim of this paper is to construct new simple and indecomposable m-factorizations of λK v for different values of m, λ and v.  ...  Factorizations arising from projective spaces There are two basic types of partitioning the point-set of finite projective spaces. Both types give factorizations of some multigraphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.26493/1855-3974.537.6bf">doi:10.26493/1855-3974.537.6bf</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fbz77g5wmba7nb3xvixspxhaym">fatcat:fbz77g5wmba7nb3xvixspxhaym</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190428145155/https://amc-journal.eu/index.php/amc/article/download/537/669" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/5f/2d/5f2d47cc56eebe5502c893214839b5de2e9442c8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.26493/1855-3974.537.6bf"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Page 4219 of Mathematical Reviews Vol. , Issue 2002F [page]

<span title="">2002</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
of complete multigraphs arising from finite geometry.  ...  In this paper, the authors use ovals and unitals of finite projective planes to construct an infinite family of one-factorizations of complete multigraphs. Michael E.  ... 
<span class="external-identifiers"> </span>
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Spectral dimension in graph models of causal quantum gravity [article]

Georgios Giasemidis
<span title="2013-10-30">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We focus on the (recurrent) multigraph approximation of the two-dimensional CDT whose ensemble measure is analytically controlled.  ...  Having defined the continuum limit, we study the reduction of the spectral dimension on more realistic toy models, the multigraph ensembles, which serve as a radial approximation of CDT.  ...  For these two reasons, we believe that the random walk on continuum multigraph ensembles captures the complete physical content of diffusion on the quantum geometry, because it is welldefined, from the  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1310.8109v1">arXiv:1310.8109v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fhsu24qahnezhakecdlhwhnefy">fatcat:fhsu24qahnezhakecdlhwhnefy</a> </span>
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Minimal Graphs in H2 x R and Their Projections

Michael Wolf
<span title="">2007</span> <i title="International Press of Boston"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/zqclzy5yebar3oqqmppyjia4le" style="color: black;">Pure and Applied Mathematics Quarterly</a> </i> &nbsp;
There has been a recent resurgence of interest in the subject of minimal surfaces in product three-manifolds, for example [HET05] .  ...  The purpose of this note is to describe a construction and some examples originating in the harmonic maps literature whose consequences for minimal surfaces seem to have escaped notice.  ...  Consider the foliation of Φ arising from the foliations of the cylinders by straight line segments orthogonal to the boundary.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4310/pamq.2007.v3.n3.a10">doi:10.4310/pamq.2007.v3.n3.a10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/egvfe2m2wra37gh6xlmdg6vxry">fatcat:egvfe2m2wra37gh6xlmdg6vxry</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190429170817/https://www.intlpress.com/site/pub/files/_fulltext/journals/pamq/2007/0003/0003/PAMQ-2007-0003-0003-a010.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0d/72/0d723473033fced7bc9efcb8c40c698c5dffb579.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4310/pamq.2007.v3.n3.a10"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

On the classification of critically fixed rational maps

Kristin Cordwell, Selina Gilbertson, Nicholas Nuechterlein, Kevin M. Pilgrim, Samantha Pinella
<span title="2015-03-19">2015</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/k76rcy45xne6jlpmdtcz26fvze" style="color: black;">Conformal Geometry and Dynamics</a> </i> &nbsp;
We discuss the dynamical, topological, and algebraic classification of rational maps f : C → C, each of whose critical points c is also a fixed-point of f , i.e., f (c) = c.  ...  Pilgrim was also supported by Simons Foundation grant 245269 and by the Department of Mathematics of Indiana University.  ...  Crane for contributing the discussion of Newton's methods in §11.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s1088-4173-2015-00275-1">doi:10.1090/s1088-4173-2015-00275-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6x3ht43pajesjn22mgi3y2aqhe">fatcat:6x3ht43pajesjn22mgi3y2aqhe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170822100451/http://www.ams.org/journals/ecgd/2015-19-04/S1088-4173-2015-00275-1/S1088-4173-2015-00275-1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/84/b8/84b87dbb88b97e772194d030070755d95fa594fc.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s1088-4173-2015-00275-1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

The maximum cut problem on blow-ups of multiprojective spaces [article]

Mauricio Junca Mauricio Velasco
<span title="2012-07-17">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We prove our results by constructing embeddings of the classes of (-1)-divisors on these varieties which are optimal for the semidefinite relaxation of the maximum cut problem on graphs proposed by Goemans  ...  More generally, we obtain bounds for the maximum cut problem for the minuscule varieties X_a,b,c:= Bl_b+c(P^c-1)^a-1 studied by Mukai and Castravet-Tevelev and show that these bounds are asymptotically  ...  Let f be an embedding obtained from the Cholesky factorization of X.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1207.4027v1">arXiv:1207.4027v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vdh5huexzfhz3dspcsyqfpu7me">fatcat:vdh5huexzfhz3dspcsyqfpu7me</a> </span>
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Integral Cayley multigraphs over Abelian and Hamiltonian groups [article]

Matt DeVos, Roi Krakovski, Bojan Mohar, Azhvan Sheikh Ahmady
<span title="2012-09-23">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We extend this result to provide a necessary and sufficient condition for a Cayley multigraph over a Hamiltonian group to be integral, in terms of character sums and the structure of the generating set  ...  It is shown that a Cayley multigraph over a group G with generating multiset S is integral (i.e., all of its eigenvalues are integers) if S lies in the integral cone over the boolean algebra generated  ...  The following theorem gives a complete characterization of which Cayley multigraphs over abelian groups are integral. Theorem 1 (Bridges, Mena [1]).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1209.5126v1">arXiv:1209.5126v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dly47mad3bf45ah3f6o5gnsukq">fatcat:dly47mad3bf45ah3f6o5gnsukq</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1209.5126/1209.5126.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1209.5126v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Integral Cayley Multigraphs over Abelian and Hamiltonian Groups

Matt DeVos, Roi Krakovski, Bojan Mohar, Azhvan Sheikh Ahmady
<span title="2013-06-30">2013</span> <i title="The Electronic Journal of Combinatorics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/v5dyak6ulffqfara7hmuchh24a" style="color: black;">Electronic Journal of Combinatorics</a> </i> &nbsp;
We extend this result to provide a necessary and sufficient condition for a Cayley multigraph over a Hamiltonian group to be integral, in terms of character sums and the structure of the generating set  ...  It is shown that a Cayley multigraph over a group $G$ with generating multiset $S$ is integral (i.e., all of its eigenvalues are integers) if $S$ lies in the integral cone over the boolean algebra generated  ...  The following theorem gives a complete characterization of which Cayley multigraphs over abelian groups are integral. Theorem 1 (Bridges, Mena [1] ).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.37236/2742">doi:10.37236/2742</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/46wqddttczgkxe4qs3vmtekita">fatcat:46wqddttczgkxe4qs3vmtekita</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180430105135/http://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p63/pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/50/2d/502d6c1a71d8d7eeb7c101988bf5de345889dcb9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.37236/2742"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

The theory of filtrations of subalgebras, standardness, and independence

A M Vershik
<span title="2017-04-30">2017</span> <i title="IOP Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pxdp4wd3hjhnzetykidnxv5xg4" style="color: black;">Russian Mathematical Surveys</a> </i> &nbsp;
One of the key notions, that of standardness, plays the role of a generalization of the notion of the independence of a sequence of random variables.  ...  The survey is devoted to the combinatorial and metric theory of filtrations, i. e., decreasing sequences of σ-algebras in measure spaces or decreasing sequences of subalgebras of certain algebras.  ...  The combinatorial structure of such multigraphs must be completely described.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1070/rm9763">doi:10.1070/rm9763</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4zk76hvxqjca5m32deo3buj5eu">fatcat:4zk76hvxqjca5m32deo3buj5eu</a> </span>
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Brill-Noether Existence on Graphs via R-Divisors, Polytopes and Lattices [article]

Madhusudan Manjunath
<span title="2019-11-26">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We study Brill-Noether existence on a finite graph using methods from polyhedral geometry and lattices.  ...  As applications, we derive upper bounds on the gonality of a graph and its R-divisor analogue.  ...  Acknowledgement: We thank Omid Amini, Spencer Backman, Matt Baker, Dhruv Ranganathan and Chi Ho Yuen for illuminating discussions on Brill-Noether theory of both curves and graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1911.11514v1">arXiv:1911.11514v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/salncbbd3ng43e2bveg67e5sny">fatcat:salncbbd3ng43e2bveg67e5sny</a> </span>
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Gap sets for the spectra of cubic graphs

Alicia Kollár, Peter Sarnak
<span title="2021-10-07">2021</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/seajmtkhgjffvcpb45y773dgre" style="color: black;">Communications of the American Mathematical Society</a> </i> &nbsp;
We study gaps in the spectra of the adjacency matrices of large finite cubic graphs.  ...  Our results show that the study of spectra of cubic, and even planar cubic, graphs is subtle and very rich.  ...  Alternatively, one can look directly at ( ) and look at the larger neighborhood that arises from each original vertex of .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/cams/3">doi:10.1090/cams/3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7cerdedcrbg5rl6l3iko5bdso4">fatcat:7cerdedcrbg5rl6l3iko5bdso4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20211014194601/https://www.ams.org/journals/cams/2021-01-01/S2692-3688-2021-00003-6/S2692-3688-2021-00003-6.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/dd/20/dd208eea57b3441d297cd708afc10cb5b7745b96.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/cams/3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

What is a design? How should we classify them?

R. A. Bailey, Peter J. Cameron
<span title="2007-07-21">2007</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/c45m6ttnaje4xbjsq7m2c6df2a" style="color: black;">Designs, Codes and Cryptography</a> </i> &nbsp;
Design theory crosses the boundary between mathematics and statistics, and includes a wide range of disparate types of design.  ...  No two manufacturers ever split it up quite the same way and every mechanic is familiar with the problem of the part you can't buy because you can't find it because the manufacturer considers it part of  ...  A chamber system of rank 2, however, does arise from a geometry.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10623-007-9092-3">doi:10.1007/s10623-007-9092-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6doe27v3onf4ppuhnqf37dx32q">fatcat:6doe27v3onf4ppuhnqf37dx32q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190302173539/http://pdfs.semanticscholar.org/a6fd/54b3f2fb1b8318c7cfdca67ee3c166ec3b47.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a6/fd/a6fd54b3f2fb1b8318c7cfdca67ee3c166ec3b47.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10623-007-9092-3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Uniqueness of Banach space valued graphons [article]

Dávid Kunszenti-Kovács
<span title="2015-12-22">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The main motivation comes from the theory of multigraph limits, where these graphons arise as the natural limit objects for convergence in a generalized homomorphism sense.  ...  In particular, limits of multigraph sequences are uniquely determined - up to measure preserving transformations - whenever the tails of the edge-distributions stay small enough.  ...  Luckily this is not a restriction here, as the multigraph constructions arising from the mixed moments preserve this property. Lemma 26.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1504.01263v2">arXiv:1504.01263v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dmbggmgjlvhjnap5npm5n3omke">fatcat:dmbggmgjlvhjnap5npm5n3omke</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200902234511/https://arxiv.org/pdf/1504.01263v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d5/3e/d53e785c2755e45618ffce30dcf860595c0d4183.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1504.01263v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Energy flow polynomials: a complete linear basis for jet substructure

Patrick T. Komiske, Eric M. Metodiev, Jesse Thaler
<span title="">2018</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/f77v2fl37rdyrodjisfjo6jbee" style="color: black;">Journal of High Energy Physics</a> </i> &nbsp;
The energy flow basis provides a systematic framework for complete investigations of jet substructure using linear methods.  ...  We introduce the energy flow polynomials: a complete set of jet substructure observables which form a discrete linear basis for all infrared- and collinear-safe observables.  ...  Since the ECFs correspond to complete graphs (see eq. (2.9)), they do not benefit from VE. Similarly, VE cannot speed up the computation of ECFGs, since the ECFGs do not have a factorable summand.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/jhep04(2018)013">doi:10.1007/jhep04(2018)013</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/smn3ve5wjbbqfl7llf64fid3lu">fatcat:smn3ve5wjbbqfl7llf64fid3lu</a> </span>
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An efficient algorithm for two-dimensional central-force rigidity [article]

Cristian F. Moukarzel
<span title="1996-12-27">1996</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Recently an integer algorithm was proposed for this problem in two dimensions, using matching methods from graph theory and Laman's theorem for two-dimensional graphs.  ...  Given a structure made up of n sites connected by b bars, the problem of recognizing which subsets of sites form rigid units is not a trivial one, because of the non-local character of rigidity in central-force  ...  D) For each edge ab in G, B(G ab ) has a complete matching from V 1 to V 2.  ... 
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