8 papers
On Semisymmetric Height and a Multidimensional Generalization of Weighted Catalan Numbers
Ryota Inagaki, Dimana Pramatarova
Weighted Catalan numbers are a class of weighted sums over Dyck paths. Well-studied for their arithmetic properties and applications to enumerative combinatorics, these numbers wer…
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…
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 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…