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+

+@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},

+  doi       = {10.1007/s11083-017-9449-9},

+  keywords  = {app},

+  publisher = {Springer Nature},

+}

+

+@Comment{jabref-meta: databaseType:bibtex;}