On problems concerning fixed-point-free permutations and on the polycirculant conjecture-a survey
Publish place: Transactions on Combinatorics، Vol: 8، Issue: 1
Publish Year: 1398
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_COMB-8-1_002
تاریخ نمایه سازی: 14 اردیبهشت 1400
Abstract:
Fixed-point-free permutations, also known as derangements, have been studied for centuries. In particular, depending on their applications, derangements of prime-power order and of prime order have always played a crucial role in a variety of different branches of mathematics: from number theory to algebraic graph theory. Substantial progress has been made on the study of derangements, many long-standing open problems have been solved, and many new research problems have arisen. The results obtained and the methods developed in this area have also effectively been used to solve other problems regarding finite vertex-transitive graphs. The methods used in this area range from deep group theory, including the classification of the finite simple groups, to combinatorial techniques. This article is devoted to surveying results, open problems and methods in this area.
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Authors
Majid Arezoomand
University of Larestan
Alireza Abdollahi
University of Isfahan
Pablo Spiga
Dipartimento di Matematica e Applicazioni, University of Milano-Bicocca,
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