31 citations · 208 across the 28 of their papers we have counts for
12 papers · 1 filter
Sums of Weighted Lattice Points of Polytopes
Jesús A. De Loera, Laura Escobar, Nathan Kaplan +1
We study the problem of counting lattice points of a polytope that are weighted by an Ehrhart quasi-polynomial of a family of parametric polytopes. As applications one can compute…
The Expected Embedding Dimension, type and weight of a Numerical Semigroup
Nathan Kaplan, Deepesh Singhal
We study statistical properties of numerical semigroups of genus as goes to infinity. More specifically, we answer a question of Eliahou by showing that as goes to infi…
Enumerating numerical sets associated to a numerical semigroup
April Chen, Nathan Kaplan, Liam Lawson +2
A numerical set is a subset of that contains and has finite complement. The atom monoid of is the set of such that .…
Numerical semigroups, polyhedra, and posets I: the group cone
Nathan Kaplan, Christopher O'Neill
Several recent papers have explored families of rational polyhedra whose integer points are in bijection with certain families of numerical semigroups. One such family, first intro…
Chip-Firing Games and Critical Groups
Darren Glass, Nathan Kaplan
In this expository article intended to be accessible to undergraduate students we introduce a finite abelian group that can be associated to any finite connected graph. This group…
Counting Numerical Semigroups
Nathan Kaplan
A numerical semigroup is an additive submonoid of the natural numbers with finite complement. The size of the complement is called the genus of the semigroup. How many numerical se…
Counting Arithmetical Structures on Paths and Cycles
Benjamin Braun, Hugo Corrales, Scott Corry +6
Let be a finite, simple, connected graph. An arithmetical structure on is a pair of positive integer vectors such that $(\mathrm{diag}(\mathbf{d})-A…
Counting Arcs in Projective Planes via Glynn's Algorithm
Nathan Kaplan, Susie Kimport, Rachel Lawrence +2
An -arc in a projective plane is a collection of distinct points in the plane, no three of which lie on a line. Formulas counting the number of -arcs in any finite projec…
Counting Finite Index Subrings of
Stanislav Atanasov, Nathan Kaplan, Benjamin Krakoff +1
We count subrings of small index of , where the addition and multiplication are defined componentwise. Let denote the number of subrings of index . For an…
Numerical Sets, Core Partitions, and Integer Points in Polytopes
Hannah Constantin, Benjamin Houston-Edwards, Nathan Kaplan
We study a correspondence between numerical sets and integer partitions that leads to a bijection between simultaneous core partitions and the integer points of a certain polytope.…
On a Cohen-Lenstra Heuristic for Jacobians of Random Graphs
Julien Clancy, Nathan Kaplan, Timothy Leake +2
In this paper, we make specific conjectures about the distribution of Jacobians of random graphs with their canonical duality pairings. Our conjectures are based on a Cohen-Lenstra…
The Proportion of Weierstrass Semigroups
Nathan Kaplan, Lynnelle Ye
We solve a problem of Komeda concerning the proportion of numerical semigroups which do not satisfy Buchweitz' necessary criterion for a semigroup to occur as the Weierstrass semig…