Vinayak Gupta

collaborators

4 papers

math.CO2026

Multiplicity bounds for nonzero upper-Laplacian eigenvalues of simplicial complexes

Vinayak Gupta

Let $K$ be a finite pure ridge-connected $d$ -dimensional simplicial complex with at least two facets, and let $m_{K} (λ)$ denote the multiplicity of a positive eigenvalue $λ$ of its u…

math.CO2026

Stability of Shifted Complexes via the Second-Moment Defect of the Up-Laplacian

Vinayak Gupta

Let $K$ be a finite pure $k$ -dimensional simplicial complex, with $k \geq 1$ , on the vertex set $[n]$ and with facet family $K_{k}$ . Let $λ_{1} (K) \geq λ_{2} (K) \geq \dots > 0$ be the nonzero eige…

math.CO2026

Spectral Bounds and Shifted Complexes: Eigenvalues of the Up-Laplacian via Face Degrees

Vinayak Gupta

Let $K$ be a finite $k$ -dimensional simplicial complex with $k \geq 1$ , and let $\Lup_{k-1}(K)$ be its $(k - 1)$ -dimensional up-Laplacian. We resolve the equality case of a conjecture o…

math.CO2025

Trees with extremal Laplacian eigenvalue multiplicity

Vinayak Gupta, Gargi Lather, R. Balaji

Let $T$ be a tree. Suppose $λ$ is an eigenvalue of the Laplacian matrix of $T$ with multiplicity $m_{T} (λ)$ . It is known that $m_{T} (λ) \leq p (T) - 1$ , where $p (T)$ is the number of…