Deepesh Singhal

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5 papers · 1 filter

math.CO2026

Distribution of Sandpile groups of random bipartite graphs

Deepesh Singhal

Fix a prime $p$ and a constant $\frac{1}{p} < I^\pm \leq 1$ . Consider the random ErdÅs--RÃ©nyi bipartite graph $G_{I^} \pm (n, u)$ with bipartition $(V_{1}, V_{2})$ of sizes $∣ V_{1} ∣ = n$ and $|V_2|=\lc…

math.CO2026

Sandpile groups of random bipartite graphs and families of distributions with the same moments

Jason Fulman, Nathan Kaplan, Deepesh Singhal +1

Recently, there has been significant interest in applying the method of moments developed by Wood and others to study distributions of finite abelian groups that arise in number th…

math.CO2026

Distribution of Sandpile groups of random directed bipartite graphs

Deepesh Singhal

Fix a prime $p$ and a constant $\frac{1}{p} < I^\pm \leq 1$ . Consider the random directed ErdÅs--RÃ©nyi bipartite graph $G (n, ⌈ I^\pm n ⌉, v)$ with bipartition $(V_{1}, V_{2})$ of si…

math.CO2026

The shape of a random numerical semigroup

Maria Bras-AmorÃ³s, Nathan Kaplan, Deepesh Singhal

We study statistical properties of random numerical semigroups of a given genus. We analyze the graph of a typical numerical semigroup, understood as a function from $N$ t…

math.CO2026

On the smallest partition associated to a numerical semigroup

Nathan Kaplan, Kaylee Kim, Cole McGeorge +2

The set of hook lengths of an integer partition $I^»$ is the complement of some numerical semigroup $S$ . There has been recent interest in studying the number of partitions with a g…