Finite Affine Groups: Cycle Indices, Hall-Littlewood Polynomials, and Probabilistic Algorithms

Hall-Littlewood多项式、仿射Schubert级数与格枚举

Hall-Littlewood polynomials, affine Schubert series, and lattice enumeration

本文引入Hall-Littlewood-Schubert级数，通过变量替换解决p-adic格枚举等问题，提供Hecke级数新公式，并作为Stanley-Reisner环Hilbert级数的q-模拟，推广Littlewood恒等式。

The Rogers-Ramanujan Identities, the Finite General Linear Groups, and the Hall-Littlewood Polynomials

The Rogers-Ramanujan identities have been studied from the viewpoints of combinatorics, number theory, affine Lie algebras, statistical mechanics, and quantum field theory. This note connects the Rogers-Ramanujan identities with the finite general linear groups and the Hall-Littlewood polynomials of symmetric function theory.

仿射群的随机自由半群

Random free semigroups of affine groups

研究可解非幂零情形下半群的随机自由性，聚焦相关仿射模型，表明自由性长期行为由阿贝尔影子决定，证明结合仿射随机游走局部收缩定理与乒乓论证。

Level, rank, and tensor growth of representations of symmetric groups

We develop a theory of levels for irreducible representations of symmetric groups of degree $n$ analogous to the theory of levels for finite classical groups. A key property of level is that the level of a character, provided it is not too big compared to $n$, gives a good lower bound on its degree, and, moreover, every character of low degree is either itself of low level or becomes so after tensoring with the sign character. Furthermore, if $l_1$ and $l_2$ satisfy a linear upper bound in $n$, then the maximal level of composition factors of the tensor product of representations of levels $l_…

基于Post陪集定理的泛幻排列的N元群

N-ary groups of panmagic permutations from the Post coset theorem

研究泛幻排列（模n皇后问题的解）的代数结构，通过Post陪集定理证明其构成二面体子群陪集的N元群推广，并揭示与数论和组合学的联系。