4 papers
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…
A mod determinant criterion for Cohen--Lenstra convergence of random -adic matrices with prescribed zero patterns
Hyungmin Jang, Nathan Kaplan, Jungin Lee +1
We study the distribution of cokernels of Haar-random matrices over the -adic integers with prescribed zero patterns, motivated by the Cohen--Lenstra heuristics. A central featu…
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 t…
The probability of isomorphic group structures of isogenous elliptic curves over finite fields
John Cullinan, Nathan Kaplan
Let l be a prime number and let E and E' be l-isogenous elliptic curves defined over Q. In this paper we determine the proportion of primes p for which E(F_p) is isomorphic to E'(F…