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On problems concerning fixed-point-free permutations and on the polycirculant conjecture-a survey | ||
Transactions on Combinatorics | ||
مقاله 2، دوره 8، شماره 1، خرداد 2019، صفحه 15-40 اصل مقاله (331.94 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22108/toc.2018.112665.1585 | ||
نویسندگان | ||
Majid Arezoomand* 1؛ Alireza Abdollahi2؛ Pablo Spiga3 | ||
1University of Larestan | ||
2University of Isfahan | ||
3Dipartimento di Matematica e Applicazioni, University of Milano-Bicocca, | ||
چکیده | ||
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. | ||
کلیدواژهها | ||
Derangements؛ Polycirculant Conjecture؛ Transitive group | ||
مراجع | ||
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