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Papi Ray

Publications and source records attributed to Papi Ray.

6 recordsLinked to original sources
arXiv2025

Characterizing finite groups whose order supergraphs satisfy a connectivity condition

Let $\Gamma$ be an undirected and simple graph. A set $ S $ of vertices in $\Gamma$ is called a {cyclic vertex cutset} of $\Gamma$ if $\Gamma - S$ is disconnected and has at least two components each containing a cycle. If $\Gamma$ has a cyclic vertex cutset, then it is said to be {cyclically separable}. For any finite group $G$, the order supergraph $\mathcal{S}(G)$ is the simple and undirected graph whose vertices are elements of $G$, and two vertices are adjacent if as elements of $G$ the order of one divides the order of the other. In this paper, we characterize the finite nilpotent groups and various non-nilpotent groups, such as the dihedral groups, the dicyclic groups, the EPPO groups, the symmetric groups, and the alternating groups, whose order supergraphs are cyclically separable.

math.CO↗
arXiv2025

A Relationship Between Character Values Of Wreath Products And The Symmetric Group

A relation between certain irreducible character values of the hyperoctahedral group $B_n$ ($\mathbb{Z}/2\mathbb{Z} \wr S_n$) and the symmetric group $S_{2n}$ was proved by F. L\"ubeck and D. Prasad in 2021. Their proof is algebraic in nature and uses Lie theory. Using combinatorial methods, R. Adin and Y. Roichman proved a similar relation between certain character values of $G\wr S_n$ and $S_{rn}$, where $G$ is an abelian group of order $r$ (generalizing the result of L\"ubeck-Prasad). Using their result, we prove yet another relation between certain irreducible character values of $G\wr S_n$ and $S_{rn}$, where $G$ is an abelian group of order $r$.

math.CO↗
arXiv2024

Forbidden subgraphs on conjugacy class graphs of groups

Let $G$ be a finite group. The commuting (resp. nilpotent) conjugacy class graph $\Gamma_{CCC}(G)$ (resp. $\Gamma_{NCC}(G)$) of $G$ is a simple graph whose vertex set consists of all non-central conjugacy classes of $G$, in which two distinct vertices $x^G$ and $y^G$ are adjacent if and only if there exist $a \in x^G$ and $b \in y^G$ such that $\langle a, b \rangle$ is an abelian (resp. nilpotent) subgroup. In this paper, we mainly investigate cographs, chordal graphs, split graphs, threshold graphs, and claw-free graphs in terms of forbidden induced subgraphs in $\Gamma_{CCC}(G)$ and $\Gamma_{NCC}(G)$. To be specific, we characterize the induced subgraphs in the commuting conjugacy class graph for symmetric groups, alternating groups, and sporadic groups. We also provide a complete classification of these properties for EPPO-groups, nilpotent groups, dihedral groups, dicyclic groups, and generalized dihedral groups in both commuting and nilpotent conjugacy class groups.

math.GR↗
arXiv2019

Local properties of Schubert Varieties in the Symplectic Grassmannian via a bounded RSK correspondence

In a paper by Ghorpade and Raghavan, they provide an explicit combinatorial description of the Hilbert function of the tangent cone at any point on a Schubert variety in the symplectic Grassmannian, by giving a certain "degree-preserving" bijection between a set of monomials defined by an initial ideal and a "standard monomial basis". We prove here that this bijection is in fact a bounded RSK correspondence.

math.CO↗