论文信息 - Symmetric functions, generalized blocks, and permutations with restricted cycle structure

Symmetric functions, generalized blocks, and permutations with restricted cycle structure

We present various techniques to count proportions of permutations with restricted cycle structure in finite permutation groups. For example, we show how a generalized block theory for symmetric groups, developed by Kulshammer, Olsson, and Robinson, can be used for such calculations. The paper includes improvements of recurrence relations of Glasby, results on average numbers of fixed points in certain permutations, and a remark on a conjecture of Robinson related to the so-called k(GV)-problem of representation theory. We extend and give alternative proofs for previous results of Erdos and Turan; Glasby; and Beals, Leedham-Green, Niemeyer, Praeger and Seress.

Attila Maróti | A. Maróti

[1] William M. Kantor,et al. On the Probability That a Group Element is p-Singular , 1995 .

[2] Andrew M. Gleason,et al. Counting Permutations , 1980, J. Comb. Theory, Ser. A.

[3] R. Stanley. What Is Enumerative Combinatorics , 1986 .

[4] A. Maróti. A Proof of a Generalized Nakayama Conjecture , 2006 .

[5] Burkhard Külshammer,et al. Generalized blocks for symmetric groups , 2003 .

[6] P. Erdos,et al. On some problems of a statistical group-theory. II , 1967 .

[7] Miklós Bóna,et al. Permutations with roots , 2000, Random Struct. Algorithms.

[8] I. G. MacDonald,et al. Symmetric functions and Hall polynomials , 1979 .

[9] Stephen P. Glasby. Using Recurrence Relations to Count Certain Elements in Symmetric Groups , 2001, Eur. J. Comb..

[10] G. James,et al. The Representation Theory of the Symmetric Group , 2009 .

[11] Robert M. Guralnick,et al. The non-coprime k(GV) problem , 2005, 1305.2725.

[12] Basil Gordon,et al. Counting Special Permutations , 1989, Eur. J. Comb..

[13] The asymptotics of $e^{P\left( z \right)}$ and the number of elements of each order in $S_n$ , 1986 .

[14] A I Pavlov,et al. ON THE NUMBER OF PERMUTATIONS OF SPECIAL FORM , 1976 .

[15] P. Erdös,et al. On some problems of a statistical group-theory. I , 1965 .

[16] Cheryl E. Praeger,et al. Permutations with Restricted Cycle Structure and an Algorithmic Application , 2002, Combinatorics, Probability and Computing.