6 papers
Chip-firing on the Lattice of Nonnegative Integer Points
Ryota Inagaki, Tanya Khovanova, Austin Luo
Chip-firing on a directed graph is a game in which chips, a discrete commodity, are placed on the vertices of the graph and are transferred between vertices. In this paper, we stud…
On Weighted and Bounded Multidimensional Catalan Numbers
Ryota Inagaki, Dimana Pramatarova
We define a weighted analog for the multidimensional Catalan numbers, obtain matrix-based recurrences for some of them, and give conditions under which they are periodic. Building…
Labeled Chip-Firing on Undirected -ary Trees
Ryota Inagaki, Aaron Lin
We explore labeled chip-firing on undirected -ary trees, trees where every vertex has degree . First, we extend known results for binary trees from Musiker and Nguyen, incl…
Labeled Chip-Firing on Directed -ary Trees and Where Chips Land
Ryota Inagaki, Tanya Khovanova, Austin Luo
Chip-firing is a combinatorial game played on a graph, in which chips are placed and dispersed on the vertices until a stable configuration is achieved. We study a chip-firing vari…
Permutation-based Strategies for Labeled Chip-Firing on -ary Trees
Ryota Inagaki, Tanya Khovanova, Austin Luo
Chip-firing is a combinatorial game on a graph, in which chips are placed and dispersed among its vertices until a stable configuration is achieved. We specifically study a chip-fi…
On Chip-Firing on Undirected Binary Trees
Ryota Inagaki, Tanya Khovanova, Austin Luo
Chip-firing is a combinatorial game played on an undirected graph in which we place chips on vertices. We study chip-firing on an infinite binary tree in which we add a self-loop t…