11 citations · 17 across the 10 of their papers we have counts for
11 papers
A note on regular polyhedra over finite fields
Caleb Ji
Grothendieck proposed a theory of regular polyhedra over finite fields in Section 4 of \textit{Esquisse d'un Programme}. He isolates certain key parameters from the automorphism gr…
Enumeration and Extensions of Word-representants
Marisa Gaetz, Caleb Ji
Given a finite word over a finite alphabet , consider the graph with vertex set and with an edge between two elements of if and only if the two elements alternate in…
Hessenberg varieties associated to ad-nilpotent ideals
Caleb Ji, Martha Precup
We consider Hessenberg varieties in the flag variety of with the property that the corresponding Hessenberg function defines an ad-nilpotent ideal. Each such Hes…
Primes with Beatty and Chebotarev conditions
Caleb Ji, Joshua Kazdan, Vaughan McDonald
We study the prime numbers that lie in Beatty sequences of the form and have prescribed algebraic splitting conditions. We prove that the density of primes…
On the Distribution of Range for Tree-Indexed Random Walks
Aaron Berger, Caleb Ji, Erik Metz
We study tree-indexed random walks as introduced by Benjamini, Häggström, and Mossel, i.e. labelings of a tree for which adjacent vertices have labels differing by 1. It is a conje…
Distinguishing Numbers and Generalizations
Caleb Ji
The distinguishing number of a graph was introduced by Albertson and Collins as a measure of the amount of symmetry contained in the graph. Tymoczko extended this definition to fai…
Brussels Sprouts, Noncrossing Trees, and Parking Functions
Caleb Ji, James Propp
We consider a variant of the game of Brussels Sprouts that, like Conway's original version, ends in a predetermined number of moves. We show that the endstates of the game are in n…
The sieving phenomenon for finite groups
Caleb Ji
The cyclic sieving phenomenon is a well-studied occurrence in combinatorics appearing when a cyclic group acts on a finite set. In this paper, we demonstrate a natural extension of…
On an Algorithm for Comparing the Chromatic Symmetric Functions of Trees
Sam Heil, Caleb Ji
It is a long-standing question of Stanley whether or not the chromatic symmetric function (CSF) distinguishes unrooted trees. Previously, the best computational result, due to Russ…
Enumerative Properties of Posets Corresponding to a Certain Class of No Strategy Games
Caleb Ji
In this paper, we consider a game beginning with a multiset of elements from a group. On a move, two elements are replaced by their sum. This is a no strategy game, and can be mode…
Chocolate Numbers
Caleb Ji, Tanya Khovanova, Robin Park +1
In this paper, we consider a game played on a rectangular gridded chocolate bar. Each move, a player breaks the bar along a grid line. Each move after that consists of…