J. Engbers

activity

20112023

most citedOn comparability of bigrassmannian permutations

5 citations · 9 across the 14 of their papers we have counts for

collaborators

16 papers

math.CO2023

Reciprocals of thinned exponential series

David Galvin, John Engbers, Clifford Smyth

The reciprocal of $e^{- x}$ has a power series about $0$ in which all coefficients are non-negative. Gessel [Reciprocals of exponential polynomials and permutation enumeration, Aust…

math.CO2019

Tomescu's graph coloring conjecture for $ℓ$ -connected graphs

John Engbers, Aysel Erey, Jacob Fox +1

Let $P_{G} (k)$ be the number of proper $k$ -colorings of a finite simple graph $G$ . Tomescu's conjecture, which was recently solved by Fox, He, and Manners, states that $P_G(k) \le k!…

math.CO2019

Colored Multipermutations and a Combinatorial Generalization of Worpitzky's Identity

John Engbers, Jay Pantone, Christopher Stocker

Worpitzky's identity expresses $n^{p}$ in terms of the Eulerian numbers and binomial coefficients: $n^{p} = i = 0 \sum p - 1 i p (p n + i) .$ Pita-Ruiz recent…

math.CO2019

Independent Sets in n-vertex k-chromatic, \ell-connected graphs

John Engbers, Lauren Keough, Taylor Short

We study the problem of maximizing the number of independent sets in $n$ -vertex $k$ -chromatic $ℓ$ -connected graphs. First we consider maximizing the total number of independent…

math.CO2017

Maximizing and minimizing the number of generalized colorings of trees

John Engbers, Christopher Stocker

We classify the trees on $n$ vertices with the maximum and the minimum number of certain generalized colorings, including conflict-free, odd, non-monochromatic, star, and star rain…

math.CO2016

Restricted Stirling and Lah number matrices and their inverses

John Engbers, David Galvin, Clifford Smyth

Given $R \subseteq N$ let ${k n}_{R}$ , $[k n]_{R}$ , and $L (n, k)_{R}$ be the number of ways of partitioning the set $[n]$ into $k$ non-empty subsets, cycles and lis…

math.CO2016

Maximizing $H$ -colorings of connected graphs with fixed minimum degree

John Engbers

For graphs $G$ and $H$ , an $H$ -coloring of $G$ is a map from the vertices of $G$ to the vertices of $H$ that preserves edge adjacency. We consider the following extremal enumerativ…

math.CO2015★ 5 cited

On comparability of bigrassmannian permutations

John Engbers, Adam Hammett

Let $S_{n}$ and $B_{n}$ denote the respective sets of ordinary and bigrassmannian (BG) permutations of order $n$ , and let $(S_{n}, \leq)$ denote the Bruha…

math.CO2015

Extremal H-colorings of trees and 2-connected graphs

John Engbers, David Galvin

For graphs $G$ and $H$ , an $H$ -coloring of $G$ is an adjacency preserving map from the vertices of $G$ to the vertices of $H$ . $H$ -colorings generalize such notions as independent…

math.CO2014

Reversible peg solitaire on graphs

John Engbers, Christopher Stocker

The game of peg solitaire on graphs was introduced by Beeler and Hoilman in 2011. In this game, pegs are initially placed on all but one vertex of a graph $G$ . If $x y z$ forms a pat…

math.CO2014

Trivial Meet and Join within the Lattice of Monotone Triangles

John Engbers, Adam Hammett

The lattice of monotone triangles $(M_{n}, \leq)$ ordered by entry-wise comparisons is studied. Let $τ_{m i n}$ denote the unique minimal element in this lattice, and $τ_{\ma…

math.CO2013★ 3 cited

Combinatorially interpreting generalized Stirling numbers

John Engbers, David Galvin, Justin Hilyard

Let $w$ be a word in alphabet ${x, D}$ with $m$ $x$ 's and $n$ $D$ 's. Interpreting " $x$ " as multiplication by $x$ , and " $D$ " as differentiation with respect to $x$ , the identity $w…

math.CO2013

Extremal H-colorings of graphs with fixed minimum degree

John Engbers

For graphs $G$ and $H$ , a homomorphism from $G$ to $H$ , or $H$ -coloring of $G$ , is a map from the vertices of $G$ to the vertices of $H$ that preserves adjacency. When $H$ is compo…

math.CO2012

Counting independent sets of a fixed size in graphs with a given minimum degree

John Engbers, David Galvin

Galvin showed that for all fixed $δ$ and sufficiently large $n$ , the $n$ -vertex graph with minimum degree $δ$ that admits the most independent sets is the complete bipartite graph…

math.CO2011

H-coloring tori

John Engbers, David Galvin

For graphs $G$ and $H$ , an $H$ -coloring of $G$ is a function from the vertices of $G$ to the vertices of $H$ that preserves adjacency. $H$ -colorings encode graph theory notions suc…

math.CO2011★ 1 cited

H-colouring bipartite graphs

John Engbers, David Galvin

For graphs $G$ and $H$ , an {\em $H$ -colouring} of $G$ (or {\em homomorphism} from $G$ to $H$ ) is a function from the vertices of $G$ to the vertices of $H$ that preserves adjacency…

Reciprocals of thinned exponential series

Tomescu's graph coloring conjecture for ℓ-connected graphs

Colored Multipermutations and a Combinatorial Generalization of Worpitzky's Identity

Independent Sets in n-vertex k-chromatic, \ell-connected graphs

Maximizing and minimizing the number of generalized colorings of trees

Restricted Stirling and Lah number matrices and their inverses

Maximizing H-colorings of connected graphs with fixed minimum degree

On comparability of bigrassmannian permutations

Extremal H-colorings of trees and 2-connected graphs

Reversible peg solitaire on graphs

Trivial Meet and Join within the Lattice of Monotone Triangles

Combinatorially interpreting generalized Stirling numbers

Extremal H-colorings of graphs with fixed minimum degree

Counting independent sets of a fixed size in graphs with a given minimum degree

H-coloring tori

H-colouring bipartite graphs

Tomescu's graph coloring conjecture for $ℓ$ -connected graphs

Maximizing $H$ -colorings of connected graphs with fixed minimum degree