Asymptotics of commuting ℓ-tuples in symmetric groups and log-concavity

被引:0
|
作者
Bringmann, Kathrin [1 ]
Franke, Johann [1 ]
Heim, Bernhard [1 ]
机构
[1] Univ Cologne, Dept Math & Comp Sci, Div Math, Weyertal 86-90, D-50931 Cologne, Germany
基金
欧洲研究理事会; 欧盟地平线“2020”;
关键词
Generating functions; Log-concavity; Partition numbers; Symmetric group; NUMBER;
D O I
10.1007/s40993-024-00562-1
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Denote by N-& ell;(n) the number of & ell;-tuples of elements in the symmetric group S-n with commuting components, normalized by the order of S-n. In this paper, we prove asymptotic formulas for N-& ell;(n). In addition, general criteria for log-concavity are shown, which can be applied to N-& ell;(n) among other examples. Moreover, we obtain a Bessenrodt-Ono type theorem which gives an inequality of the form c(a)c(b) > c(a + b) for certain families of sequences c(n).
引用
收藏
页数:19
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