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The hafnian of Toeplitz matrices of a special type, perfect matchings and Bessel polynomials [article]

Dmitry Efimov
<span title="2019-04-18">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
An interpretation of the obtained results is given in the language of perfect matchings and Bessel polynomials.  ...  We present a simple and convenient analytical formula for efficient exact computation of the hafnian of Toeplitz matrices of a special type.  ...  The resulting formula can be used to find the number of perfect matchings of special graphs, for example, complements of the path graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1904.08651v1">arXiv:1904.08651v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xhwcirl33rcexcmotz3zifqs2e">fatcat:xhwcirl33rcexcmotz3zifqs2e</a> </span>
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Perfect commuting graphs [article]

John R. Britnell, Nick Gill
<span title="2015-10-22">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We classify the finite quasisimple groups whose commuting graph is perfect and we give a general structure theorem for finite groups whose commuting graph is perfect.  ...  Then the commuting graph of G is not perfect. The proof that follows shows, in addition, that the commuting graph of GL 3 (q) is non-perfect for q > 2. Proof.  ...  Let α and β be distinct non-zero elements of F q . Then the five matrices .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1309.2237v2">arXiv:1309.2237v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ay7wsljqtzb2ja6oyw2wa4ubfi">fatcat:ay7wsljqtzb2ja6oyw2wa4ubfi</a> </span>
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Perfect state transfer of a qudit over underlying networks of group association schemes [article]

M. A. Jafarizadeh, R. Sufiania, S. F. Taghavia, E. Baratia
<span title="2009-03-10">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
a large class of cubelike graphs (e.g., the hypercube) which are the Cayley graphs of the elementary abelian group Z_2^n.  ...  Therefore, PST over the underlying networks of the group association schemes over all the groups with non-trivial centers such as the abelian groups, the dihedral group D_2n with even n, the Clifford group  ...  [17] , state transfer over spin chains of arbitrary spin has been discussed so that an arbitrary unknown qudit be transferred through a chain with rather a good fidelity by the natural dynamics of the  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0901.4504v2">arXiv:0901.4504v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/e5fm3b35snaizl7a6ctn77qzgu">fatcat:e5fm3b35snaizl7a6ctn77qzgu</a> </span>
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Discretization of continuous-time quantum walks via the staggered model with Hamiltonians [article]

Gabriel Coutinho, Renato Portugal
<span title="2018-05-22">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This connection provides examples of perfect state transfer and instantaneous uniform mixing in the staggered model.  ...  We characterize a close connection between the continuous-time quantum-walk model and a discrete-time quantum-walk version, based on the staggered model with Hamiltonians in a class of Cayley graphs, which  ...  the adjacency matrix can be written as a sum of commuting matrices related to a graph factorization.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1701.03423v2">arXiv:1701.03423v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bh243hviy5dtzenqjdzbewcdbm">fatcat:bh243hviy5dtzenqjdzbewcdbm</a> </span>
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Perfect commuting graphs

John R. Britnell, Nick Gill
<span title="2017-01-01">2017</span> <i title="Walter de Gruyter GmbH"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/x5j4wze4zjdupdzdb4hcrhmyia" style="color: black;">Journal of group theroy</a> </i> &nbsp;
AbstractWe classify the finite quasisimple groups whose commuting graph is perfect and we give a general structure theorem for finite groups whose commuting graph is perfect.  ...  The second author was a visitor at the University of Bristol while this work was undertaken and would like to thank the members of the Department of Mathematics for their hospitality.  ...  Then the commuting graph of G is not perfect. The proof that follows shows, in addition, that the commuting graph of GL 3 .q/ is non-perfect for q > 2. Proof.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1515/jgth-2016-0024">doi:10.1515/jgth-2016-0024</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/62ykkrfpqve57hbzzvqfodj7iq">fatcat:62ykkrfpqve57hbzzvqfodj7iq</a> </span>
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Book announcements

<span title="">1977</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
Combinatorics of finite geometries (A. Barlotri); On finite non-commutative affine spaces (J. And&). Coding Theory. Weight enumerators of codes (M.4.A.  ...  Perfect Graphs (C. Rerge). Transversal Theory iind Graphs (R.A. Brualdi). On the Shortest Route Through a Network (G.B. Dantzig). Electrical Netwofk Models (W.J. D&in).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0012-365x(77)90015-2">doi:10.1016/0012-365x(77)90015-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dikvo2vidfabxoixyesdwnvkla">fatcat:dikvo2vidfabxoixyesdwnvkla</a> </span>
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Column-partitioned matrices over rings without invertible transversal submatrices [article]

Stephan Foldes, Erkko Lehtonen
<span title="2006-11-18">2006</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Let the columns of a p × q matrix M over any ring be partitioned into n blocks, M = [M_1, ..., M_n].  ...  form and in all but at most m-1 blocks QM_i the last m entries of each column are either all zero or they include a non-zero non-unit.  ...  Acknowledgements The authors thank Miguel Couceiro and Jenő Szigeti for useful discussions of the subject.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0611551v1">arXiv:math/0611551v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fdqyixabn5e2ze3w3zpvzdlvny">fatcat:fdqyixabn5e2ze3w3zpvzdlvny</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-math0611551/math0611551.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] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/58/1d/581da323f266e9e29e44a48ee451e31353d28b74.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0611551v1" 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>

From Independent Sets and Vertex Colorings to Isotropic Spaces and Isotropic Decompositions: Another Bridge Between Graphs and Alternating Matrix Spaces

Xiaohui Bei, Shiteng Chen, Ji Guan, Youming Qiao, Xiaoming Sun, Michael Wagner
<span title="2020-01-10">2020</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cjckxhgqp5dobfucnrxpxnsy4u" style="color: black;">Innovations in Theoretical Computer Science</a> </i> &nbsp;
A similar connection between bipartite graphs and matrix spaces plays a key role in the recent resolutions of the non-commutative rank problem (Garg-Gurvits-Oliveira-Wigderson, FOCS 2016; Ivanyos-Qiao-Subrahmanyam  ...  In the 1970's, Lovász built a bridge between graphs and alternating matrix spaces, in the context of perfect matchings (FCT 1979).  ...  The techniques supporting the solutions to the non-commutative rank problem are reminiscent of the corresponding techniques for the perfect matching problem on bipartite graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.itcs.2020.8">doi:10.4230/lipics.itcs.2020.8</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/innovations/BeiCGQS20.html">dblp:conf/innovations/BeiCGQS20</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/s57l6dzewbfc5ljjxsg7xsv4fq">fatcat:s57l6dzewbfc5ljjxsg7xsv4fq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201211014631/https://drops.dagstuhl.de/opus/volltexte/2020/11693/pdf/LIPIcs-ITCS-2020-8.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/9c/65/9c653d524828ebfb9db54b1fded3020ce7de9c2d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.itcs.2020.8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

LDPC Quantum Codes [article]

Nikolas P. Breuckmann, Jens Niklas Eberhardt
<span title="2021-03-10">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this Perspective we discuss a particular class of quantum codes called low-density parity-check (LDPC) quantum codes.  ...  We introduce the zoo of LDPC quantum codes and discuss their potential for making quantum computers robust against noise.  ...  Let R ⊂ F × 2 be a commutative subalgebra of the ring of × matrices over F 2 . Now let A ∈ R n×m and B ∈ R k×l be matrices with entries in the algebra R.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2103.06309v1">arXiv:2103.06309v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nrzxvirsdfhhvhqtbj7rqzghrm">fatcat:nrzxvirsdfhhvhqtbj7rqzghrm</a> </span>
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A switching approach for perfect state transfer over a scalable and routing enabled network architecture with superconducting qubits [article]

Siddhant Singh
<span title="2020-07-03">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In addition, we present the numerical study of signed graphs under Corona product of graphs and show few examples where PST is established, in contrast to pre-existing results in the literature for disproof  ...  We then generalise this switching scheme over arbitrary number of qubits where also this routing feature of PST between any two vertices is possible.  ...  Perfect state transfer over greater distances Perfect state transfer over arbitrary distances is impossible for a simple unmodulated spin chain (limited to n = 2 and n = 3 only!).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.02682v1">arXiv:2007.02682v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/23im3qhcvjbxpi3racwh5e3gd4">fatcat:23im3qhcvjbxpi3racwh5e3gd4</a> </span>
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Asymptotic behaviour of certain sets of associated prime ideals of Ext-modules

K. Khashyarmanesh, F. Khosh-Ahang
<span title="2007-12-18">2007</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ukh3ohtqy5finnf2mzhsgss4mq" style="color: black;">Manuscripta mathematica</a> </i> &nbsp;
In this paper, we first give some results of min-projective and minflat modules. Then, we study the class of min-projective on some rings such as cotorsion, von Neumann regular and perfect rings.  ...  Let R be a commutative ring and M be a unitary R-module. Our aim is to investigate semiprime submodule of a module and to consider some of its properties.  ...  Finally, we study the diameter and coloring of annihilating-ideal graphs. Let M be a finite module over a commutative noetherian ring R.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00229-007-0152-9">doi:10.1007/s00229-007-0152-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pf2qggcagjhong4oyvwj2ikwsi">fatcat:pf2qggcagjhong4oyvwj2ikwsi</a> </span>
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Control by quantum dynamics on graphs

Chris Godsil, Simone Severini
<span title="2010-05-14">2010</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/iedolmzeofgc3ezyedga7h4eba" style="color: black;">Physical Review A. Atomic, Molecular, and Optical Physics</a> </i> &nbsp;
We address the study of controllability of a closed quantum system whose dynamical Lie algebra is generated by adjacency matrices of graphs.  ...  We characterize a large family of graphs that renders a system controllable. The key property is a novel graph-theoretic feature consisting of a particularly disordered cycle structure.  ...  and Alastair Kay for very valuable conversation about quantum control theory and for reading earlier drafts; Domenico D'Alessandro for several important remarks; Alessandro Cosentino for drawing the graphs  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreva.81.052316">doi:10.1103/physreva.81.052316</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/w2ohtjvchvamha5quagdfk4b24">fatcat:w2ohtjvchvamha5quagdfk4b24</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200827172142/https://arxiv.org/pdf/0910.5397v2.pdf" title="fulltext PDF download [not primary version]" 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] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d9/3c/d93ca0cd3884fc136ffeae068610a0d3d0f1bfc9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreva.81.052316"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> aps.org </button> </a>

Solution of tetrahedron equation and cluster algebras

P. Gavrylenko, M. Semenyakin, Y. Zenkevich
<span title="">2021</span> <i title="Springer Science and Business Media LLC"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/f77v2fl37rdyrodjisfjo6jbee" style="color: black;">Journal of High Energy Physics</a> </i> &nbsp;
Finally, we embed this integrable system into the double Bruhat cell of a Poisson-Lie group, show how triangular decomposition can be used to extend our approach to the general non-symmetric Newton polygons  ...  The tetrahedron transformation is then identified with a sequence of four mutations.  ...  We say that perfect network N in disk D is the result of gluing of N 1 over 1 to N 2 over 2 if disks are glued D = (D 1 D 2 )/ 1 ∼ 2 in such a way that the grey vertices from A 1 are glued to B 2 , and  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/jhep05(2021)103">doi:10.1007/jhep05(2021)103</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/agcc7gl75vcjfppwpdzkxa7z2e">fatcat:agcc7gl75vcjfppwpdzkxa7z2e</a> </span>
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Random Walks on Dynamic Graphs: Mixing Times, Hitting Times, and Return Probabilities

Thomas Sauerwald, Luca Zanetti, Michael Wagner
<span title="2019-07-08">2019</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pf6v2q6ji5h7birkbrtpdc2uhy" style="color: black;">International Colloquium on Automata, Languages and Programming</a> </i> &nbsp;
Finally, we investigate properties of random walks on dynamic graphs that are not always connected: we relate their convergence to stationarity to the spectral properties of an average of transition matrices  ...  For random walks on dynamic connected graphs for which the stationary distribution does not change over time, we show that their behaviour is in a certain sense similar to static graphs.  ...  constant spectral gap), one over {1, . . . , n}, the other over {n + 1, . . . , 2n}, while at even t, G (t) is a perfect matching between {1, . . . , n} and {n + 1, . . . , 2n}.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.icalp.2019.93">doi:10.4230/lipics.icalp.2019.93</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/icalp/SauerwaldZ19.html">dblp:conf/icalp/SauerwaldZ19</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2tzvaq2gxveorlvghva6l73ec4">fatcat:2tzvaq2gxveorlvghva6l73ec4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220307212224/https://drops.dagstuhl.de/opus/volltexte/2019/10669/pdf/LIPIcs-ICALP-2019-93.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/ea/6e/ea6e1a6c078a844198667af6e3d0a84877bc1928.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.icalp.2019.93"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

From independent sets and vertex colorings to isotropic spaces and isotropic decompositions [article]

Xiaohui Bei, Shiteng Chen, Ji Guan, Youming Qiao, Xiaoming Sun
<span title="2019-09-22">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A similar connection between bipartite graphs and matrix spaces plays a key role in the recent resolutions of the non-commutative rank problem (Garg-Gurvits-Oliveira-Wigderson, FOCS 2016; Ivanyos-Qiao-Subrahmanyam  ...  In the 1970's, Lov\'asz built a bridge between graphs and alternating matrix spaces, in the context of perfect matchings (FCT 1979).  ...  G. was partly supported by the National Key R&D Program of China (Grant No:  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1904.03950v2">arXiv:1904.03950v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oyvehwj5ubhkrfptmeza3suzkm">fatcat:oyvehwj5ubhkrfptmeza3suzkm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200930152615/https://arxiv.org/pdf/1904.03950v2.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/63/e4/63e4032f788813af0ff6bebf3b72bda1f5cd7601.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1904.03950v2" 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>
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