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Publications (6)

math.CO2025

Combinatorial Identities Using the Matrix Tree Theorem

Nayana Shibu Deepthi, Chanchal Kumar

In this paper, we explore some interesting applications of the matrix tree theorem. In particular, we present a combinatorial interpretation of a distribution of $(n - 1)^{n - 1}$ , in…

math.CO2020

Standard Monomials of 1-Skeleton Ideals of Graphs and Their Signless Laplace Matrices

Chanchal Kumar, Gargi Lather, Amit Roy

Let $G$ be a (multi) graph on the vertex set $V = {0, 1, \dots, n}$ with root $0$ . The $G$ -parking function ideal $M_{G}$ is a monomial ideal in the polynomial ring $R=\math…

math.CO2020

Skeleton Ideals of Certain Graphs, Standard Monomials and Spherical Parking Functions

Chanchal Kumar, Gargi Lather, Sonica

Let $G$ be an (oriented) graph on the vertex set $V = {0, 1, \dots, n}$ with root $0$ . Postnikov and Shapiro associated a monomial ideal $M_{G}$ in the polynomial ring $…

math.CO2026

Enumeration of certain subsets of uprooted trees and spherical parking functions

Nayana Shibu Deepthi, Chanchal Kumar, Gargi Lather

Spherical $G$ -parking functions are a distinguished subset of standard monomials, arising from the skeleton ideals of the $G$ -parking function ideal. Explicit enumeration formulas…

math.CO2020

Integer Sequences and Monomial Ideals

Chanchal Kumar, Amit Roy

Let $S_{n}$ be the set of all permutations of $[n] = {1, \dots, n}$ and let $W$ be the subset consisting of permutations $I ¨ \in S_{n}$ avoiding 132 and 312-pattern…

math.RA2009

Group Rings that are Additively Generated by Idempotents and Units

Dinesh Khurana, Chanchal Kumar

We study clean group rings and also the group rings whose every element is a sum of two units. We also prove that if R is an Abelian exchange ring and G is a locally finite group,…