Erik Insko

activity

20112026

most citedAffine pavings of regular nilpotent Hessenberg varieties and intersection theory of the Peterson variety

7 citations · 22 across the 23 of their papers we have counts for

collaborators

28 papers

math.GM2026

Limit Cases And Strategy In Chutes and Ladders

Vincent Ciarcia, Erik Insko

We analyze what happens to the average duration of a game of Chutes and Ladders as the probability of rolling $δ \in {1, 2, 3, 4, 5, 6}$ approaches 100%. We utilize Markov models, and…

math.AG2024

Regular Hessenberg varieties for the minimal indecomposable Hessenberg space

Erik Insko, Martha Precup, Alexander Woo

This paper investigates the geometry of regular Hessenberg varieties associated with the minimal indecomposable Hessenberg space in the flag variety of a complex reductive group. T…

math.AG2022

On singularity and normality of regular nilpotent Hessenberg varieties

Hiraku Abe, Erik Insko

Regular nilpotent Hessenberg varieties form an important family of subvarieties of the flag variety, which are often singular and sometimes not normal varieties. Like Schubert vari…

math.PR2022

Tipsy cop and tipsy robber: collisions of biased random walks on graphs

Pamela E. Harris, Erik Insko, Florian Lehner

Introduced by Harris, Insko, Prieto Langarica, Stoisavljevic, and Sullivan, the \emph{tipsy cop and drunken robber} is a variant of the cop and robber game on graphs in which the r…

math.CO2022★ 1 cited

Partial permutohedra

Roger E. Behrend, Federico Castillo, Anastasia Chavez +4

Partial permutohedra are lattice polytopes which were recently introduced and studied by Heuer and Striker. For positive integers $m$ and $n$ , the partial permutohedron $\mathcal{P…

math.CO2022

A combinatorial model for lane merging

Viktoriya Bardenova, Erik Insko, Katie Johnson +1

A two lane road approaches a stoplight. The left lane merges into the right just past the intersection. Vehicles approach the intersection one at a time, with some drivers always c…

math.CO2021

On $(t, r)$ broadcast domination of directed graphs

Pamela E. Harris, Peter Hollander, Erik Insko

A dominating set of a graph $G$ is a set of vertices that contains at least one endpoint of every edge on the graph. The domination number of $G$ is the order of a minimum dominati…

math.CO2021★ 1 cited

Markov models for the tipsy cop and robber game on graphs

Viktoriya Bardenova, Vincent Ciarcia, Erik Insko

In this paper we analyze and model three open problems posed by Harris, Insko, Prieto-Langarica, Stoisavljevic, and Sullivan in 2020 concerning the tipsy cop and robber game on gra…

math.CO2020

Tipsy cop and drunken robber: a variant of the cop and robber game on graphs

Pamela Harris, Erik Insko, Alicia Prieto-Langarica +2

Motivated by a biological scenario illustrated in the YouTube video \url{ https://www.youtube.com/watch?v=Z_mXDvZQ6dU} where a neutrophil chases a bacteria cell moving in random di…

math.CO2020

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…

math.AG2018

A formula for the cohomology and $K$ -class of a regular Hessenberg variety

Erik Insko, Julianna Tymoczko, Alexander Woo

Hessenberg varieties are subvarieties of the flag variety parametrized by a linear operator $X$ and a nondecreasing function $h$ . The family of Hessenberg varieties for regular $X$ …

math.CO2018

A Variant on the Feline Josephus Problem

Shaun Sullivan, Erik Insko

In the Feline Josephus problem, soldiers stand in a circle, each having $ℓ$ `lives'. Going around the circle, a life is taken from every $k$ th soldier; soldiers with 0 lives rem…

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.RT2017

Computing weight $q$ -multiplicities for the representations of the simple Lie algebras

Pamela E. Harris, Erik Insko, Anthony Simpson

The multiplicity of a weight $μ$ in an irreducible representation of a simple Lie algebra $g$ with highest weight $λ$ can be computed via the use of Kostant's weight mul…

math.AG2017

The singular locus of semisimple Hessenberg varieties

Erik Insko, Martha Precup

Although regular semisimple Hessenberg varieties are smooth and irreducible, semisimple Hessenberg varieties are not necessarily smooth in general. In this paper we determine the i…

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

Upper broadcast domination of toroidal grids and a classification of diametrical trees

Erik Insko, Bethany Kubik, Candice Price

A broadcast on a graph $G = (V, E)$ is a function $f : V \to {0, 1, \dots, diam (G)}$ satisfying $f (v) \leq e (v)$ for all $v \in V$ , where $e (v)$ denotes the eccentricit…

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…

math.CO2015★ 3 cited

The $q$ -analog of Kostant's partition function and the highest root of the classical Lie algebras

Pamela E. Harris, Erik Insko, Mohamed Omar

Kostant's partition function counts the number of ways to represent a particular vector (weight) as a nonnegative integral sum of positive roots of a Lie algebra. For a given weigh…

math.CO2015

A Terrible Expansion of the Determinant

Erik Insko, Katie Johnson, Shaun Sullivan

From a transfer formula in multivariate finite operator calculus, comes an expansion for the determinant similar to Ryser's formula for the permanent. Although this one contains ma…

math.GR2015★ 6 cited

Peaks Sets of Classical Coxeter Groups

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

We say a permutation $π = π_{1} π_{2} \dots π_{n}$ in the symmetric group $S_{n}$ has a peak at index $i$ if $π_{i - 1} < π_{i} > π_{i + 1}$ and we let $P(π)=\{i \in \{1, 2, \ldots, n\} \, \v…

math.AC2014

Proceedings of the 4th annual Underrepresented Students in Topology and Algebra Research Symposium (USTARS 2014)

USTARS Organizing Committee, :, Jeannine Abiva +5

This volume represents the proceedings of the 4th annual meetings of the Underrepresented Students in Topology and Algebra Research Symposium (USTARS 2014), held on 11-13 April 201…

math.RA2014

A new characterization of the exceptional Lie algebras

Pamela Harris, Erik Insko

For a simple Lie algebra, over $C$ , we consider the weight which is the sum of all simple roots and denote it $α ~$ . We formally use Kostant's weight multiplicity form…

math.CO2014★ 2 cited

On (t,r) Broadcast Domination Numbers of Grids

David Blessing, Erik Insko, Katie Johnson +1

The domination number of a graph $G = (V, E)$ is the minimum cardinality of any subset $S \subset V$ such that every vertex in $V$ is in $S$ or adjacent to an element of $S$ . Findin…