139 citations · 249 across the 31 of their papers we have counts for
32 papers
The sandpile model on the complete split graph: -Schröder polynomials, sawtooth polyominoes, and a cycle lemma
Henri Derycke, Mark Dukes, Yvan Le Borgne
This paper studies sorted recurrent configurations of the Abelian sandpile model on the complete split graph. We introduce two natural toppling processes, CTI and ITC toppling, on…
Difference ascent sequences
Mark Dukes, Bruce Sagan
Let alpha = a_1 a_2 ... a_n be a sequence of nonnegative integers. The ascent set of alpha, Asc(alpha), consists of all indices k where a_{k+1} > a_k. An ascent sequence is alpha w…
An Ising model having permutation spin motivated by a permutation complexity measure
Mark Dukes
In this paper we define a variant of the Ising model in which spins are replaced with permutations. The energy between two spins is a function of the relative disorder of one spin,…
Counting tournament score sequences
Anders Claesson, Mark Dukes, Atli Fannar Franklín +1
The score sequence of a tournament is the sequence of the out-degrees of its vertices arranged in nondecreasing order. The problem of counting score sequences of a tournament with…
A simple declarative model of the Federal Disaster Assistance Policy -- modelling and measuring transparency
Mark Dukes
In this paper we will provide a quantitative analysis of a simple model of the Federal Disaster Assistance policy from the viewpoint of three different stakeholders. This quantitat…
Stakeholder utility measures for declarative processes and their use in process comparisons
Mark Dukes
We present a method for calculating and analyzing stakeholder utilities of processes that arise in, but are not limited to, the social sciences. These areas include business proces…