7 papers
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…
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…