Deepesh Singhal

activity

20192026

most citedDensity of Numerical sets associated to a Numerical semigroup

2 citations · 3 across the 18 of their papers we have counts for

collaborators

18 papers

math.CO2026

Distribution of Sandpile groups of random bipartite graphs

Deepesh Singhal

Fix a prime $p$ and a constant $\frac{1}{p} < α \leq 1$ . Consider the random Erdős--Rényi bipartite graph $G_{α} (n, u)$ with bipartition $(V_{1}, V_{2})$ of sizes $∣ V_{1} ∣ = n$ and $|V_2|=\lceilα…

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 $\frac{1}{p} < α \leq 1$ . Consider the random directed Erdős--Rényi bipartite graph $G (n, ⌈ α n ⌉, v)$ with bipartition $(V_{1}, V_{2})$ of sizes…

math.CO2026

The shape of a random numerical semigroup

Maria Bras-Amorós, 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.AG2025

Largest zero-dimensional intersection of $r$ degree $d$ hypersurfaces

Yuxin Lin, Deepesh Singhal

Suppose we have $r$ hypersurfaces in $P^{m}$ of degree $d$ , whose defining polynomials are linearly independent, and their intersection has dimension $0$ . Then what is the l…

math.CO2025

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 $λ$ is the complement of some numerical semigroup $S$ . There has been recent interest in studying the number of partitions with a gi…

math.NT2025

The $p$ -rank stratification of the moduli space of double covers of a fixed elliptic curve

Kevin Chang, Dušan Dragutinović, Steven R. Groen +3

In this paper we investigate the $p$ -rank stratification of the moduli space of curves of genus $g$ that admit a double cover to a fixed elliptic curve $E$ in characteristic $p > 2$ .…

math.AG2024

Non- $p$ -ordinary smooth abelian covers of $P^{1}$

Yuxin Lin, Elena Mantovan, Deepesh Singhal

Given a family of odd abelian covers of $P^{1}$ and a prime $p$ of good reduction, in [1], under some assumptions, we computed the generic Newton polygon (resp. Ekedahl-Oort…

math.AG2023

On a conjecture of Beelen, Datta and Ghorpade for the number of points of varieties over finite fields

Deepesh Singhal, Yuxin Lin

Consider a finite field $F_{q}$ and positive integers $d, m, r$ with $1 \leq r \leq (d m + d)$ . Let $S_{d} (m)$ be the $F_{q}$ vector space of all homogeneous polynomia…

math.AG2023

Abelian covers of $P^{1}$ of $p$ -ordinary Ekedahl-Oort type

Yuxin Lin, Elena Mantovan, Deepesh Singhal

Given a family of abelian covers of $P^{1}$ and a prime $p$ of good reduction, by considering the associated Deligne--Mostow Shimura variety, we obtain lower bounds for the…

math.NT2023

Denisty questions in rings of the form $O_{K} [γ] \cap K$

Deepesh Singhal, Yuxin Lin

We fix a number field $K$ and study statistical properties of the ring $O_{K} [γ] \cap K$ as $γ$ varies over algebraic numbers of a fixed degree $n \geq 2$ . Given $k \geq 1$ , w…

math.NT2022

Primes in denominators of algebraic numbers

Deepesh Singhal, Yuxin Lin

Denote the set of algebraic numbers as $Q$ and the set of algebraic integers as $Z$ . For $γ \in Q$ , consider its irreducib…

math.CO2022

The Expected Embedding Dimension, type and weight of a Numerical Semigroup

Nathan Kaplan, Deepesh Singhal

We study statistical properties of numerical semigroups of genus $g$ as $g$ goes to infinity. More specifically, we answer a question of Eliahou by showing that as $g$ goes to infi…

math.CO2022

Enumerating numerical sets associated to a numerical semigroup

April Chen, Nathan Kaplan, Liam Lawson +2

A numerical set $T$ is a subset of $N_{0}$ that contains $0$ and has finite complement. The atom monoid of $T$ is the set of $x \in N_{0}$ such that $x + T \subseteq T$ .…

math.CO2021

Frobenius allowable gaps of Generalized Numerical Semigroups

Deepesh Singhal, Yuxin Lin

A generalised numerical semigroup (GNS) is a submonoid $S$ of $N^{d}$ for which the complement $N^{d} ∖ S$ is finite. The points in the complement $\mathbb{N}^…

math.CO2020★ 1 cited

Complementary Numerical Sets

Matthew Guhl, Jazmine Juarez, Vadim Ponomarenko +2

A numerical set $S$ is a cofinite subset of $N$ which contains $0$ . We use the natural bijection between numerical sets and Young diagrams to define a numerical set $\wide…

math.CO2020

Distribution of genus among numerical semigroups with fixed Frobenius number

Deepesh Singhal

A numerical semigroup is a sub-semigroup of the natural numbers that has a finite complement. The size of its complement is called the genus and the largest number in the complemen…

math.CO2019★ 2 cited

Density of Numerical sets associated to a Numerical semigroup

Deepesh Singhal, Yuxin Lin

A numerical set is a co-finite subset of the natural numbers that contains zero. Its Frobenius number is the largest number in its complement. Each numerical set has an associated…

Distribution of Sandpile groups of random bipartite graphs

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

Distribution of Sandpile groups of random directed bipartite graphs

The shape of a random numerical semigroup

Largest zero-dimensional intersection of r degree d hypersurfaces

On the smallest partition associated to a numerical semigroup

The p-rank stratification of the moduli space of double covers of a fixed elliptic curve

Non-p-ordinary smooth abelian covers of P1

On a conjecture of Beelen, Datta and Ghorpade for the number of points of varieties over finite fields

Abelian covers of P1 of p-ordinary Ekedahl-Oort type

Denisty questions in rings of the form OK​[γ]∩K

Primes in denominators of algebraic numbers

The Expected Embedding Dimension, type and weight of a Numerical Semigroup

Enumerating numerical sets associated to a numerical semigroup

Frobenius allowable gaps of Generalized Numerical Semigroups

Complementary Numerical Sets

Distribution of genus among numerical semigroups with fixed Frobenius number

Density of Numerical sets associated to a Numerical semigroup

Largest zero-dimensional intersection of $r$ degree $d$ hypersurfaces

The $p$ -rank stratification of the moduli space of double covers of a fixed elliptic curve

Non- $p$ -ordinary smooth abelian covers of $P^{1}$

Abelian covers of $P^{1}$ of $p$ -ordinary Ekedahl-Oort type

Denisty questions in rings of the form $O_{K} [γ] \cap K$