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On the Representations of Γ1-Nonderanged permutation group g_p

Advances in Pure Mathematics 2016年第9期6卷 608-614页

作者： Ibrahim A. Aminu Ejima Ojonugwa Kazeem O. Aremu Usmanu Danfodiyo University Sokoto Nigeria

Representation theory is concerned with the ways of explaining or visualizing a group as a group of matrices. In this paper, we extend the permutation pattern of to a two-line notation. We consider the representations of this non-deranged permutation group(p ≥ 5 and p a prime). Also we reveal some interesting properties and results of the character of where .

关键词： Representation Non-Deranged permutation group Γ1-permutation group Fgp-Module Character

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M?bius Regular Maps of Order pq

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Acta Mathematica Sinica,English Series 2019年第5期35卷 690-702页

作者： Fu Rong WANG Shao Fei DU School of Information Beijing Wuzi University School of Mathematical Sciences Capital Normal University

M?bius regular maps are surface embeddings of graphs with doubled edges such that(i)the automorphism group of the embedding acts regularly on flags and(ii) each doubled edge is a center of a M?bius band on the surface... 详细信息

关键词： Mobius regular maps regular embedding permutation group

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Efficient remote preparation of arbitrary twoand three-qubit states via the χ state

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Chinese Physics B 2014年第9期23卷 100-106页

作者：马松雅罗明星 School of Mathematics and Information Sciences Henan University School of Information Science and Technology Southwest Jiaotong University State Key Laboratory of Information Security Chinese Academy of Sciences

The application of χ state are investigated in remote state preparation （RSP）. By constructing useful measurement bases with the aid of Hurwitz matrix equation, we propose several RSP schemes of arbitrary two- and three-qubit states via the χ state as the entangled resource. It is shown that the original state can be successfully prepared with the probability 100% and 50% for real coefficients and complex coefficients, respectively. For the latter case, the special ensembles with unit success probability are discussed by the permutation group. It is worth mentioning that the novel measurement bases have no restrictions on the coefficients of the prepared state, which means that the proposed schemes are more applicable.

关键词： χ state remote state preparation Hurwitz matrix equation measurement basis permutation group

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On fixity of arc-transitive graphs

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Science China Mathematics 2021年第12期64卷 2603-2610页

作者： Florian Lehner Primoz Potocnik Pablo Spiga Institute of Discrete Mathematics Graz University of TechnologyGraz 8010Austria Faculty of Mathematics and Physics University of LjubljanaLjubljana 1000Slovenia Dipartimento di Matematica Pura e Applicata University of Milano-BicoccaMilano 20126Italy

The relative xity of a permutation group is the maximum proportion of the points xed by a non-trivial element of the group,and the relative xity of a graph is the relative xity of its automorphism group,viewed as a permutation group on the vertex-set of the graph.We prove in this paper that the relative xity of connected 2-arc-transitive graphs of a xed valence tends to 0 as the number of vertices grows to in nity.We prove the same result for the class of arc-transitive graphs of a xed prime valence,and more generally,for any class of arc-transitive locally-L graphs,where L is a xed quasiprimitive graph-restrictive permutation group.

关键词： permutation group xity minimal degree graph automorphism group vertex-transitive arc-transitive xed points

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