Orbifold Euler Characteristics and the Number of Commuting M-tuples in the Symmetric Groups

A NOTE ON THE COMMUTING GRAPHS OF A CONJUGACY CLASS IN SYMMETRIC GROUPS

The commuting graph of a group is a graph with vertexes set of a subset of a group and two element are adjacent if they commute. The aim of this paper is to obtain the automorphism group of the commuting graph of a conjugacy class in the symmetric groups. The clique number, coloring number, independent number, and diameter of these graphs are also computed.

Probability of Mutually Commuting N-Tuples in Some Classes of Compact Groups

Orbifold Euler Characteristics for Dual Invertible Polynomials

To construct mirror symmetric Landau–Ginzburg models, P. Berglund, T. Hübsch and M. Henningson considered a pair (f, G) consisting of an invertible polynomial f and an abelian group G of its symmetries together with a dual pair (f̃ , G̃). Here we study the reduced orbifold Euler characteristics of the Milnor fibers of f and f̃ with the actions of the groups G and G̃ respectively and show that they ...

Sharply $(n-2)$-transitive Sets of Permutations

Let $S_n$ be the symmetric group on the set $[n]={1, 2, ldots, n}$. For $gin S_n$ let $fix(g)$ denote the number of fixed points of $g$. A subset $S$ of $S_n$ is called $t$-emph{transitive} if for any two $t$-tuples $(x_1,x_2,ldots,x_t)$ and $(y_1,y_2,ldots ,y_t)$ of distinct elements of $[n]$, there exists $gin S$ such that $x_{i}^g=y_{i}$ for any $1leq ileq t$ and additionally $S$ is called e...

Twisted Index Theory on Orbifold Symmetric Products and the Fractional Quantum Hall Effect

We extend the noncommutative geometry model of the fractional quantum Hall effect, previously developed by Mathai and the first author, to orbifold symmetric products. It retains the same properties of quantization of the Hall conductance at integer multiples of the fractional Satake orbifold Euler characteristics. We show that it also allows for interesting composite fermions and anyon represe...