Priyanshu Pant

collaborators

7 papers

math.PR2026

Anticoncentration of Complex Gaussian Hafnians

Priyanshu Pant

Let $G_{2 n}$ be a complex symmetric random matrix whose entries above the diagonal are independent standard circular complex Gaussians, and let $H_{n} = haf (G_{2 n})$ . We…

math.CO2026

An Odd Pfaffian Number

Priyanshu Pant, Ranveer Singh

The Pfaffian number of a graph is the minimum number of Pfaffians needed to obtain its perfect-matching polynomial by linear combination. In 2009, Norine conjectured that every Pfa…

math.CO2026

Counterexamples to a Conjecture on Laplacian Ratios of Trees

Priyanshu Pant

For a graph $G$ with no isolated vertices, its Laplacian ratio is defined as \[ π(G)=\frac{\operatorname{per}(L(G))}{\prod_{v\in V(G)} d(v)}, \] where $L(G)$ is the Laplacian m…

math.CO2026

Exponential Lower Bounds for the Pfaffian Number of Graphs

Priyanshu Pant, Ranveer Singh

Galluccio--Loebl and Tesler showed that the perfect-matching polynomial of a graph embedded in an orientable surface of genus $g$ can be written as a linear combination of at most…

math.CO2026

Structural Classes for Chollet's Permanent Conjecture

Priyanshu Pant, Ranveer Singh

In 1982, Chollet conjectured that $per (A \circ B) \leq per (A) per (B)$ for Hermitian positive semidefinite matrices $A, B$ , where $\circ$ de…

math.CO2026

Permanental Energy of Graphs

Priyanshu Pant, Ranveer Singh

For a simple graph $G$ with adjacency matrix $A (G)$ , let $π (G, x) := per (x I - A (G))$ be its permanental polynomial with roots $μ_{1}, \dots, μ_{n} \in C$ , and define the pe…

math.CO2025

Permanental Analog of the Rank-Nullity Theorem for Symmetric Matrices

Priyanshu Pant, Surabhi Chakrabartty, Ranveer Singh

The rank of an n x n matrix A is equal to the size of its largest square submatrix with a nonzero determinant, and it can be computed in O(n^2.37) time. Analogously, the size of th…