Priyanshu Pant

collaborators

5 papers

math.CO2026

Exponential Lower Bounds for the Pfaffian Number of Graphs

Priyanshu Pant, Ranveer Singh

The Fisher--Kasteleyn--Temperley (FKT) algorithm counts perfect matchings in planar graphs in polynomial time using a single Pfaffian computation. Galluccio--Loebl and Tesler exten…

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 \[ Ï(G)=\frac{\operatorname{per}(L(G))}{\prod_{v\in V(G)} d(v)}, \] where $L(G)$ is the Laplacian…

math.CO2026

On Chollet's Permanent Conjecture for Graph Laplacians

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 $\circ$ denotes the Hadamard…

math.CO2026

Permanental Energy of Graphs

Priyanshu Pant, Ranveer Singh

For a simple graph $G$ with adjacency matrix $A (G)$ , let $I ¨ (G, x) := per (x I - A (G))$ be its permanental polynomial with roots $I^¼_{1}, \dots, I^¼_{n} \in C$ , and define the…

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…