4 papers · 1 filter
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…