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% Encoding: windows-1252
@Article{BBCDLP15euler,
author = {Banaian, Esther and Butler, Steve and Cox, Christopher and Davis, Jeffrey and Landgraf, Jacob and Ponce, Scarlitte},
title = {A generalization of {E}ulerian numbers via rook placements},
journal = {Involve},
year = {2017},
volume = {10},
number = {4},
pages = {691-705},
month = {03},
keywords = {pub},
owner = {Chris},
url = {http://arxiv.org/abs/1508.03673},
}
@Article{BBCDLP15prime,
author = {Banaian, Esther and Butler, Steve and Cox, Christopher and Davis, Jeffrey and Landgraf, Jacob and Ponce, Scarlitte},
title = {Counting prime juggling patterns},
journal = {Graphs and Combinatorics},
year = {2016},
volume = {32},
number = {5},
pages = {1675-1688},
month = {9},
keywords = {pub},
owner = {Chris},
url = {http://arxiv.org/abs/1508.05296}
}
@Article{BCDHKLMMNPS15choose,
author = {Berikkyzy, Zhanar and Cox, Christopher and Dairyko, Michael and Hogenson, Kirsten and Kumbhat, Mohit and Lidick{\'y}, Bernard and Messerschmidt, Kacy and Moss, Kevin and Nowak, Kathleen and Palmowski, Kevin and Stolee, Derrick},
title = {{$(4,2)$}-choosability of planar graphs with forbidden substructures},
journal = {Graphs and Combinatorics},
year = {2017},
volume = {33},
number = {4},
pages = {751-787},
month = {07},
keywords = {pub},
owner = {Chris},
timestamp = {2015.08.05},
url = {http://arxiv.org/abs/1512.03787},
}
@Article{CDDKRT15hanabi,
author = {Cox, Christopher and De Silva, Jessica and DeOrsey, Philip and Kenter, Franklin and Retter, Troy and Tobin, R. Joshua},
title = {How to make the perfect fireworks display: {T}wo strategies for {H}anabi},
journal = {Mathematics Magazine},
year = {2015},
volume = {88},
number = {5},
pages = {323-336},
month = {12},
abstract = {The game of \emph{Hanabi} is a multi-player cooperative card game which has many similarities to a mathematical `hat guessing game.' In \emph{Hanabi}, players do not know the cards in their own hand and must rely on the actions of the other players to communicate information.
This paper presents two strategies for \emph{Hanabi}. Results from computer simulation demonstrate that both strategies perform well. In particular, one strategy achieves a perfect score of 25 points 75 percent of the time.},
keywords = {pub},
owner = {Chris},
timestamp = {2015.05.05},
}
@Article{CFMR15potram,
author = {Cox, Christopher and Ferrara, Michael and Martin, Ryan R. and Reineger, Benjamin},
title = {Chv{\'a}tal-type results for degree sequence {R}amsey numbers},
journal = {Preprint available as arXiv:1510.04843},
year = {2015},
month = {5},
abstract = {A sequence of nonnegative integers $\pi =(d_1,d_2,...,d_n)$ is {\it graphic} if there is a (simple) graph $G$ of order $n$ having degree sequence $\pi$. In this case, $G$ is said to {\it realize} or be a {\it realization of} $\pi$. Given a graph $H$, a graphic sequence $\pi$ is \textit{potentially $H$-graphic} if there is some realization of $\pi$ that contains $H$ as a subgraph.
In this paper, we consider a degree sequence analogue to classical graph Ramsey numbers. For graphs $H_1$ and $H_2$, the \textit{potential-Ramsey number} $\rpot(H_1,H_2)$ is the minimum integer $N$ such that for any $N$-term graphic sequence $\pi$, either $\pi$ is potentially $H_1$-graphic or the complementary sequence $\overline{\pi}=(N-1-d_N,\dots, N-1-d_1)$
is potentially $H_2$ graphic.
We prove that if $s\ge 2$ is an integer and $T_t$ is a tree of order $t\ge 9(s-2)$ and then $$\rpot(T_t, K_s) = t+s-2.$$ This result, which is best possible up to the constant on $s-2$, is a degree sequence analogue to a classical 1977 result of Chv\'{a}tal on the graph Ramsey number of trees vs.\ cliques. To obtain this theorem, we prove a sharp condition that ensures an arbitrary graph packs with a forest, which is likely to be of independent interest.},
owner = {Chris},
timestamp = {2015.05.05},
url = {http://arxiv.org/abs/1510.04843},
}
@Article{CS16orram,
Title = {Ordered {R}amsey numbers of loose paths and matchings},
Author = {Cox, Christopher and Stolee, Derrick},
Journal = {Discrete Mathematics},
Year = {2016},
Month = {2},
Number = {2},
Pages = {499-505},
Volume = {339},
Abstract = {For a $k$-uniform hypergraph $G$ with vertex set $\{1,\ldots,n\}$, the ordered Ramsey number $\OR{t}{G}$ is the least integer $N$ such that every $t$-coloring of the edges of the complete $k$-uniform graph on vertex set $\{1,\ldots,N\}$ contains a monochromatic copy of $G$ whose vertices follow the prescribed order.
Due to this added order restriction, the ordered Ramsey numbers can be much larger than the usual graph Ramsey numbers.
We determine that the ordered Ramsey numbers of loose paths under a monotone order grows as a tower of height two less than the maximum degree in terms of the number of edges.
We also extend theorems of Conlon, Fox, Lee, and Sudakov [Ordered Ramsey numbers, arXiv:1410.5292] on the ordered Ramsey numbers of 2-uniform matchings to provide upper bounds on the ordered Ramsey number of $k$-uniform matchings under certain orderings.},
Keywords = {pub},
Owner = {Chris},
Timestamp = {2015.05.05},
Url = {http://www.sciencedirect.com/science/article/pii/S0012365X15003477}
}
@Article{briggscox17,
author = {Joseph Briggs and Christopher Cox},
title = {Inverting the {T}ur{\' a}n problem},
abstract = {Classical questions in extremal graph theory concern the asymptotics of $\operatorname{ex}(G, \mathcal{H})$ where $\mathcal{H}$ is a fixed family of graphs and $G=G_n$ is taken from a "standard" increasing sequence of host graphs $(G_1, G_2, \dots)$, most often $K_n$ or $K_{n,n}$. Inverting the question, we can instead ask how large $|E(G)|$ can be with respect to $\operatorname{ex}(G,\mathcal{H})$. We show that the standard sequences indeed maximize $|E(G)|$ for some choices of $\mathcal{H}$, but not for others. Many interesting questions and previous results arise very naturally in this context, which also, unusually, gives rise to sensible extremal questions concerning multigraphs and non-uniform hypergraphs.},
date = {2017-11-06},
eprint = {1711.02082v2},
eprintclass = {math.CO},
eprinttype = {arXiv},
file = {online:http\://arxiv.org/pdf/1711.02082v2:PDF},
keywords = {sub},
}
@Article{Bukh2018,
author = {Boris Bukh and Christopher Cox},
title = {On a fractional version of {H}aemers' bound},
abstract = {In this note, we present a fractional version of Haemers' bound on the Shannon capacity of a graph, which is originally due to Blasiak. This bound is a common strengthening of both Haemers' bound and the fractional chromatic number of a graph. We show that this fractional version outperforms any bound on the Shannon capacity that could be attained through Haemers' bound. We show also that this bound is multiplicative, unlike Haemers' bound.},
date = {2018-02-01},
eprint = {1802.00476v1},
eprintclass = {cs.IT},
eprinttype = {arXiv},
file = {online:http\://arxiv.org/pdf/1802.00476v1:PDF},
keywords = {sub},
}
@Article{Bukh2018a,
author = {Boris Bukh and Christopher Cox},
title = {Nearly orthogonal vectors and small antipodal spherical codes},
abstract = {How can $d+k$ vectors in $\mathbb{R}^d$ be arranged so that they are as close to orthogonal as possible? In particular, define $\theta(d,k):=\min_X\max_{x\neq y\in X}|\langle x,y\rangle|$ where the minimum is taken over all collections of $d+k$ unit vectors $X\subseteq\mathbb{R}^d$. In this paper, we focus on the case where $k$ is fixed and $d\to\infty$. In establishing bounds on $\theta(d,k)$, we find an intimate connection to the existence of systems of ${k+1\choose 2}$ equiangular lines in $\mathbb{R}^k$. Using this connection, we are able to pin down $\theta(d,k)$ whenever $k\in\{1,2,3,7,23\}$ and establish asymptotics for general $k$. The main tool is an upper bound on $\mathbb{E}_{x,y\sim\mu}|\langle x,y\rangle|$ whenever $\mu$ is an isotropic probability mass on $\mathbb{R}^k$, which may be of independent interest. Our results translate naturally to the analogous question in $\mathbb{C}^d$. In this case, the question relates to the existence of systems of $k^2$ equiangular lines in $\mathbb{C}^k$, also known as SIC-POVM in physics literature.},
date = {2018-03-08},
eprint = {1803.02949v1},
eprintclass = {math.CO},
eprinttype = {arXiv},
file = {online:http\://arxiv.org/pdf/1803.02949v1:PDF},
keywords = {sub},
}
@Article{Cox2018,
author = {Christopher Cox and Derrick Stolee},
title = {Ramsey Numbers for Partially-Ordered Sets},
journal = {Order},
year = {2018},
month = {jan},
keywords = {app},
publisher = {Springer Nature},
}
@Comment{jabref-meta: databaseType:bibtex;}
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