A. Diaz-Lopez

collaborators

3 papers

math.CO2017

Descent polynomials

Alexander Diaz-Lopez, Pamela E. Harris, Erik Insko +2

Let $n$ be a nonnegative integer and $I$ be a finite set of positive integers. In 1915, MacMahon proved that the number of permutations in the symmetric group $S_{n}$ with…

math.CO2017

Peaks on Graphs

Alexander Diaz-Lopez, Lucas Everham, Pamela E. Harris +3

Given a graph $G$ with $n$ vertices and a bijective labeling of the vertices using the integers $1, 2, \dots, n$ , we say $G$ has a peak at vertex $v$ if the degree of $v$ is greater…

math.CO2016

A proof of the peak polynomial positivity conjecture

Alexander Diaz-Lopez, Pamela E. Harris, Erik Insko +1

We say that a permutation $π = π_{1} π_{2} \dots π_{n} \in S_{n}$ has a peak at index $i$ if $π_{i - 1} < π_{i} > π_{i + 1}$ . Let $P (π)$ denote the set of indices where $π$ has…