2 papers
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.RA2026
Positive definite, positive semidefinite and totally positive matrices over finite fields
Arvind Ayyer, Shubhanshu Prasad
Motivated by the equivalent definitions of positive definite (resp. positive semidefinite) matrices over real and complex fields, we give four (resp. five) inequivalent definitions…