3 papers
math.CO2025
Knuth's big-chooser matchbox process: the case of many matchboxes
Mark Dukes, Andrew Mullins
Banach's matchbox problem considers the setting of two matchboxes that each initially contain the same number of matches. Boxes are chosen with equal probability and a match remove…
math.CO2025
Characterizing traces of processes defined by precedence and response constraints: an order theory approach
Mark Dukes, Anton Sohn
In this paper we consider a general system of activities that can, but do not have to, occur. This system is governed by a set containing two types of constraints: precedence and r…
math.CO2024
A note on the lacking polynomial of the complete bipartite graph
Amal Alofi, Mark Dukes
The lacking polynomial is a graph polynomial introduced by Chan, Marckert, and Selig in 2013 that is closely related to the Tutte polynomial of a graph. It arose by way of a genera…