7 papers · 1 filter
Generalized chip firing and critical groups of arithmetical structures on trees
Kassie Archer, Alexander Diaz-Lopez, Darren Glass +1
Chip firing provides a way to study the sandpile group (also known as the Jacobian) of a graph. We use a generalized version of chip firing to bound the number of invariant factors…
Arithmetical Structures on Coconut Trees
Alexander Diaz-Lopez, Brian Ha, Pamela E. Harris +3
If G is a finite connected graph, then an arithmetical structure on is a pair of vectors with positive integer entries such that $(\diag(\mathbf{d})…
A formula for enumerating permutations with a fixed pinnacle set
Alexander Diaz-Lopez, Pamela E. Harris, Isabella Huang +2
In 2017 Davis, Nelson, Petersen, and Tenner pioneered the study of pinnacle sets of permutations and asked whether there exists a class of operations, which applied to a permutatio…
Arithmetical structures on bidents
Kassie Archer, Abigail Bishop, Alexander Diaz-Lopez +3
An arithmetical structure on a finite, connected graph is a pair of vectors with positive integer entries for which $(\operatorname{diag}(\mathbf{d})…
Descent polynomials
Alexander Diaz-Lopez, Pamela E. Harris, Erik Insko +2
Let be a nonnegative integer and be a finite set of positive integers. In 1915, MacMahon proved that the number of permutations in the symmetric group with…
Peaks on Graphs
Alexander Diaz-Lopez, Lucas Everham, Pamela E. Harris +3
Given a graph with vertices and a bijective labeling of the vertices using the integers , we say has a peak at vertex if the degree of is greater…