Ranveer Singh

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20242026

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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

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…