Andrew Pendleton

collaborators

3 papers

math.NT2026

Multiplicities of eigenvalues and quadratic representations of integers

Siqi Fu, Andrew Pendleton

We study the set $M$ of all multiplicities of non-zero eigenvalues for the Laplace operator on a two-dimensional rectangle or torus. We show that for a rectangle with the side leng…

math.CO2026

Enumeration and Distribution of Permutation Rows and Columns in Equi- $n$ -Squares

Andrew Pendleton

We introduce consecutive equi- $n$ -squares, a variant of equi- $n$ -squares in which at least one row or column forms a fixed permutation of ${1, \dots, n}$ , taken for concreteness to…

math.NT2025

Improved Bounds for the Index Conjecture in Zero-Sum Theory

Andrew Pendleton

The Index Conjecture in zero-sum theory states that when $n$ is coprime to $6$ and $k$ equals $4$ , every minimal zero-sum sequence of length $k$ modulo $n$ has index $1$ . While oth…

Multiplicities of eigenvalues and quadratic representations of integers

Enumeration and Distribution of Permutation Rows and Columns in Equi-n-Squares

Improved Bounds for the Index Conjecture in Zero-Sum Theory

Enumeration and Distribution of Permutation Rows and Columns in Equi- $n$ -Squares