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Graphical complexity of products of permutation groups

Mariusz Grech, Artur Jeż, Andrzej Kisielewicz
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
In particular, we consider how such representations for various products of permutation groups can be obtained from representations of factors and how the degree of complexity increases in such constructions  ...  In this paper we study representations of permutation groups as automorphism groups of colored graphs and supergraphs.  ...  constructions do not increase graphical complexity of permutation groups.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.disc.2007.04.004">doi:10.1016/j.disc.2007.04.004</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3sfge6t75jbcxajjnyvadzomwi">fatcat:3sfge6t75jbcxajjnyvadzomwi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171003102405/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/c9a/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDAxMjM2NXgwNzAwMTc2OA%3D%3D.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/3c/16/3c169f4665ef6f67060afd23178d095360f2ff67.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.disc.2007.04.004"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Enumeration under group action: Unsolved graphical enumeration problems, IV

Frank Harary
<span title="">1970</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/57vjscp3tbep5m7txvss2kcz44" style="color: black;">Journal of Combinatorial Theory</a> </i> &nbsp;
Thus three different binary operations on permutation groups, the sum, product, and power group, are defined and the structure of each is investigated.  ...  Applications of the corresponding theorems for enumeration under group action are provided. We conclude with a table of 27 current unsolved problems in graphical enumeration.  ...  The theorem corresponding to the product of two groups is somewhat more complex [4] . PRODUCT GROUP ENUMERATION THEOREM.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0021-9800(70)80003-5">doi:10.1016/s0021-9800(70)80003-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4hpgrd7le5gyjp7o6qrtkfcqiu">fatcat:4hpgrd7le5gyjp7o6qrtkfcqiu</a> </span>
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On the partition functions induced by iterated (k-folded) wreath product groups

Alejandro Chinea
<span title="">2015</span> <i title="Hikari, Ltd."> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/c3nnemz5kjgl5ahgbpptliliqi" style="color: black;">Advanced Studies in Theoretical Physics</a> </i> &nbsp;
Wreath products are group-theoretic constructions that have been used to model symmetries in a whole variety of research disciplines.  ...  The goal of this paper is to calculate the partition functions induced by these algebraic structures when organized iteratively under the symmetries imposed by the permutation and cyclic groups.  ...  For instance, figure 2 graphically represents an iterated wreath product operation of k levels when the group components under consideration are action groups.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.12988/astp.2015.5989">doi:10.12988/astp.2015.5989</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pkinewlkpbdylncqr6wswuocb4">fatcat:pkinewlkpbdylncqr6wswuocb4</a> </span>
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On the geometry of van Kampen diagrams of graph products of groups [article]

Anthony Genevois
<span title="2019-02-11">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this article, we propose a geometric framework dedicated to the study of van Kampen diagrams of graph products of groups.  ...  As a consequence, a graph product of groups with linear conjugacy length functions has linear conjugacy length function as well.  ...  We begin by defining graph products of groups. Graph products of groups.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1901.04538v2">arXiv:1901.04538v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/upxpct3hsffm7mwmrqd5xx4hgu">fatcat:upxpct3hsffm7mwmrqd5xx4hgu</a> </span>
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Page 693 of Mathematical Reviews Vol. 37, Issue 3 [page]

<span title="">1969</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;
P. 3798 The graphical solution of trinomial and tetranomial algebraic equations with complex coefficients. (Russian) Taskent. Gos. Univ. Nauén. Trudy Vyp. 245 (1964), 11-16.  ...  This paper describes graphical methods (and an instrument based thereon) for obtaining complex roots of the three-term and four-term equations Z"+A,Z+A,=0, Z"+A,Z"+A,Z+A,=0, where the coefficients A, are  ... 
<span class="external-identifiers"> </span>
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Page 3456 of Mathematical Reviews Vol. , Issue 88g [page]

<span title="">1988</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;
The problem of finding one- and two-valent graphic groups is easily solved. Here the author describes all trivalent graphic primitive minimal transitive permutation groups of finite degree.  ...  A permutation group G of degree n is called a k-valent graphic group if there exists an n-vertex regular graph I of valency k whose group of automorphisms AutTI is similar to G.  ... 
<span class="external-identifiers"> </span>
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The Lie Representation of the Complex Unit Sphere [article]

Jason Glowney
<span title="2018-03-18">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We describe our derivation process, which involves the creation of a finite group by using permutation matrices, and the exponentiation of the adjoint form of the subset representing the generators of  ...  We take clues from the 2-dimensional complex rotation matrix to present, what we believe, is a true representation of the Lie group for the six-dimensional complex unit sphere and proceed to study its  ...  In our permutation matrix, the imaginary permutations "b", "d" and "f" comprise the basis of the group , by way of the fact that with the products of just these three permutations, we can arrive at all  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1707.03283v8">arXiv:1707.03283v8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ubnbrp4kfbej5ckkr3dfmzktii">fatcat:ubnbrp4kfbej5ckkr3dfmzktii</a> </span>
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Random Redundant Soft-In Soft-Out Decoding of Linear Block Codes

Thomas Halford, Keith Chugg
<span title="">2006</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ux5tf45dtrgptnezraiii73msm" style="color: black;">2006 IEEE International Symposium on Information Theory</a> </i> &nbsp;
presented a practically realizable algorithm that applies only to cyclic codes while Kothiyal et al. presented an algorithm that, while applicable to arbitrary linear block codes, does not imply a low-complexity  ...  Simulation results illustrate the successful application of the random redundant iterative decoding algorithm to the extended binary Golay code.  ...  Generation of Random Permutation Group Elements Algorithm 1 requires the efficient generation of random elements of the permutation group of a code.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/isit.2006.261947">doi:10.1109/isit.2006.261947</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/isit/HalfordC06.html">dblp:conf/isit/HalfordC06</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xanxzfj5nfe2lmh42tfsk4tibe">fatcat:xanxzfj5nfe2lmh42tfsk4tibe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170812080833/http://ultra.usc.edu/assets/002/36888.pdf?origin=publication_detail" 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/57/aa/57aa5b423d393f04c04c914d1a196e698953ae65.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/isit.2006.261947"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Classifications and canonical forms of tensor product expressions in the presence of permutation symmetries [article]

Zhendong Li, Sihong Shao, Wenjian Liu
<span title="2018-12-18">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In these processes, a key step is the collection of tensor product terms that can be found identical by utilizing permutation symmetries of tensors or relabeling dummy indices, which is usually achieved  ...  Complicated mathematical equations involving products of tensors with permutation symmetries, frequently encountered in fields such as general relativity and quantum chemistry (e.g., equations in high-order  ...  In Figure 5 Tensor Ext graphical representation of tensor products.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1604.06156v2">arXiv:1604.06156v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/u3alj6e7ubg3repznu6oemfoym">fatcat:u3alj6e7ubg3repznu6oemfoym</a> </span>
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Markov Chains on Orbits of Permutation Groups [article]

Mathias Niepert
<span title="2012-06-28">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
First, we present a scalable approach to computing generating sets of permutation groups representing the symmetries of graphical models.  ...  We establish an insightful connection between model symmetries and rapid mixing of orbital Markov chains. Thus, we present the first lifted MCMC algorithm for probabilistic graphical models.  ...  Acknowledgments Many thanks to Guy Van den Broeck, Kristian Kersting, Martin Mladenov, and Babak Ahmadi for insightful discussions concerning lifted inference, to Jürgen Müller for helpful remarks on the product  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1206.5396v2">arXiv:1206.5396v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/avzi7bbwjjh7lmgifxfpvza5ny">fatcat:avzi7bbwjjh7lmgifxfpvza5ny</a> </span>
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Markov Chains on Orbits of Permutation Groups [article]

Mathias Niepert
<span title="2014-08-09">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
First, we present a scalable approach to computing generating sets of permutation groups representing the symmetries of graphical models.  ...  We establish an insightful connection between model symmetries and rapid mixing of orbital Markov chains. Thus, we present the first lifted MCMC algorithm for probabilistic graphical models.  ...  Acknowledgments Many thanks to Guy Van den Broeck, Kristian Kersting, Martin Mladenov, and Babak Ahmadi for insightful discussions concerning lifted inference, to Jürgen Müller for helpful remarks on the product  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1408.2052v1">arXiv:1408.2052v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fzzijyrcfzbg7bi2tppjqhve3i">fatcat:fzzijyrcfzbg7bi2tppjqhve3i</a> </span>
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Reducing Computational Complexity of Tensor Contractions via Tensor-Train Networks [article]

Ilya Kisil, Giuseppe G. Calvi, Kriton Konstantinidis, Yao Lei Xu, Danilo P. Mandic
<span title="2021-09-08">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
However, depending on the dimensionality of the underlying tensors, the TCP also comes at the price of high computational complexity in tensor manipulation.  ...  A key tool underpinning multi-linear manipulation of tensors and tensor networks is the standard Tensor Contraction Product (TCP).  ...  COMPUTATIONAL COMPLEXITY OF TTCP We shall first illustrate the advantages of the graphical TTCP through an example, followed by the analysis of computational complexity. Example 2.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2109.00626v2">arXiv:2109.00626v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/n6e5ftk6k5aphgvjfjmkimxcem">fatcat:n6e5ftk6k5aphgvjfjmkimxcem</a> </span>
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Graphics Generator for Physics Research [chapter]

Eliza Consuela
<span title="2012-07-25">2012</span> <i title="InTech"> Automation </i> &nbsp;
product of two vectors, matrix decomposition, permutation of matrices, resolution the linear systems.  ...  vector, the product of a vector and a matrix, the product of a matrix line and the column of another matrix, matrices decomposition, permuting, the resolution of the linear systems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5772/50013">doi:10.5772/50013</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/p7bi5bfzqvazvkmnhalw4zqoom">fatcat:p7bi5bfzqvazvkmnhalw4zqoom</a> </span>
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Page 20 of Mathematical Reviews Vol. , Issue 94c [page]

<span title="">1994</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;
Dixon, Constructing representations of finite groups (105-112); Derek F. Holt and Sarah Rees, A graphics sys- tem for displaying finite quotients of finitely presented groups (113-126); William M.  ...  Sims, Complexity issues in infinite group theory (277-286); Leonard H. Soicher, GRAPE: a system for computing with graphs and groups (287-291); Bryant W.  ... 
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On the automorphism groups of strongly regular graphs I

László Babai
<span title="">2014</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cjckxhgqp5dobfucnrxpxnsy4u" style="color: black;">Proceedings of the 5th conference on Innovations in theoretical computer science - ITCS &#39;14</a> </i> &nbsp;
Our main result is that if X is a s. r. graph then, with straightforward exceptions, the degree of the largest alternating group involved in the automorphism group Aut(X) (as a quotient of a subgroup)  ...  The design of isomorphism tests for various classes of structures is intimately connected with the study of the automorphism groups of those structures.  ...  Now Aut(X) = S k D5 (the wreath product of S k by the dihedral group D5).  ... 
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