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math.CO2026
Asymmetric Catalan and Shi Hyperplane Arrangements
Sucharita Biswas, Shubhanshu Prasad, Shushma Rani
In this paper, we study the regions of asymmetric extensions of the Catalan and Shi arrangements. We first determine the characteristic polynomials using the finite field method, t…
math.CO2025
Marked multi-colorings and marked chromatic polynomials of hypergraphs and subspace arrangements
Chaithra P, Shushma Rani, R. Venkatesh
We introduce the concepts of marked multi-colorings, marked chromatic polynomials, and marked (multivariate) independence series for hypergraphs. We show that the coefficients of t…
math.CO2021
A study on free roots of Borcherds-Kac-Moody Lie Superalgebras
Shushma Rani, G. Arunkumar
Let be a Borcherds-Kac-Moody Lie superalgebra (BKM superalgebra in short) with the associated graph . Any such is constructed from a free Lie superal…