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| -rw-r--r-- | content/submitted.bib | 11 |
4 files changed, 133 insertions, 125 deletions
diff --git a/content/contact.tex b/content/contact.tex index bc971f5..ac0f0d6 100644 --- a/content/contact.tex +++ b/content/contact.tex @@ -2,4 +2,4 @@ Carnegie Mellon University\\ Pittsburgh, PA 15213\\ \texttt{cocox@andrew.cmu.edu}\\ -\url{math.cmu.edu/~cocox}% +\href{http://math.cmu.edu/~cocox/}{\texttt{math.cmu.edu/\~{}cocox/}}% diff --git a/content/papers.bib b/content/papers.bib new file mode 100644 index 0000000..b182933 --- /dev/null +++ b/content/papers.bib @@ -0,0 +1,132 @@ +@article {jBC19, + AUTHOR = {Briggs, Joseph and Cox, Christopher}, + TITLE = {Inverting the {T}ur\'{a}n problem}, + JOURNAL = {Discrete Math.}, + FJOURNAL = {Discrete Mathematics}, + VOLUME = {342}, + YEAR = {2019}, + NUMBER = {7}, + PAGES = {1865--1884}, + ISSN = {0012-365X}, + MRCLASS = {05C35}, + MRNUMBER = {3937748}, + DOI = {10.1016/j.disc.2019.03.005}, + URL = {https://doi.org/10.1016/j.disc.2019.03.005}, +} + +@article {bBC19, + AUTHOR = {Bukh, Boris and Cox, Christopher}, + TITLE = {On a fractional version of {H}aemers’ bound}, + JOURNAL = {IEEE Transactions on Information Theory}, + VOLUME = {65}, + NUMBER = {6}, + PAGES = {3340--3348}, +} + +@article {CS18, + AUTHOR = {Cox, Christopher and Stolee, Derrick}, + TITLE = {Ramsey numbers for partially-ordered sets}, + JOURNAL = {Order}, + FJOURNAL = {Order. A Journal on the Theory of Ordered Sets and its + Applications}, + VOLUME = {35}, + YEAR = {2018}, + NUMBER = {3}, + PAGES = {557--579}, + ISSN = {0167-8094}, + MRCLASS = {05C55 (05C65 06A07)}, + MRNUMBER = {3861400}, +MRREVIEWER = {Zilin Jiang}, + DOI = {10.1007/s11083-017-9449-9}, + URL = {https://doi.org/10.1007/s11083-017-9449-9}, +} + +@article {BCDHKLMMNPS17, + 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 F. and Stolee, Derrick}, + TITLE = {{$(4,2)$}-choosability of planar graphs with forbidden + structures}, + JOURNAL = {Graphs Combin.}, + FJOURNAL = {Graphs and Combinatorics}, + VOLUME = {33}, + YEAR = {2017}, + NUMBER = {4}, + PAGES = {751--787}, + ISSN = {0911-0119}, + MRCLASS = {05C15 (05C10)}, + MRNUMBER = {3665686}, + DOI = {10.1007/s00373-017-1812-5}, + URL = {https://doi.org/10.1007/s00373-017-1812-5}, +} + +@article {BBCDLP17, + 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}, + FJOURNAL = {Involve. A Journal of Mathematics}, + VOLUME = {10}, + YEAR = {2017}, + NUMBER = {4}, + PAGES = {691--705}, + ISSN = {1944-4176}, + MRCLASS = {05A15 (05A05)}, + MRNUMBER = {3630311}, +MRREVIEWER = {Volker Strehl}, + DOI = {10.2140/involve.2017.10.691}, + URL = {https://doi.org/10.2140/involve.2017.10.691}, +} + +@article {BBCDLP16, + 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 Combin.}, + FJOURNAL = {Graphs and Combinatorics}, + VOLUME = {32}, + YEAR = {2016}, + NUMBER = {5}, + PAGES = {1675--1688}, + ISSN = {0911-0119}, + MRCLASS = {05A05 (05A15 05A30)}, + MRNUMBER = {3543189}, +MRREVIEWER = {Zhicong Lin}, + DOI = {10.1007/s00373-016-1711-1}, + URL = {https://doi.org/10.1007/s00373-016-1711-1}, +} + +@article {CD16, + AUTHOR = {Cox, Christopher and Stolee, Derrick}, + TITLE = {Ordered {R}amsey numbers of loose paths and matchings}, + JOURNAL = {Discrete Math.}, + FJOURNAL = {Discrete Mathematics}, + VOLUME = {339}, + YEAR = {2016}, + NUMBER = {2}, + PAGES = {499--505}, + ISSN = {0012-365X}, + MRCLASS = {05C55 (05C65)}, + MRNUMBER = {3431360}, + DOI = {10.1016/j.disc.2015.09.026}, + URL = {https://doi.org/10.1016/j.disc.2015.09.026}, +} + +@article {CDDKRT15, + AUTHOR = {Cox, Christopher and De Silva, Jessica and DeOrsey, Philip and + Kenter, Franklin H. J. and Retter, Troy and Tobin, Josh}, + TITLE = {How to make the perfect fireworks display: two strategies for + {\it {H}anabi}}, + JOURNAL = {Math. Mag.}, + FJOURNAL = {Mathematics Magazine}, + VOLUME = {88}, + YEAR = {2015}, + NUMBER = {5}, + PAGES = {323--336}, + ISSN = {0025-570X}, + MRCLASS = {91A46 (91A12)}, + MRNUMBER = {3470682}, + DOI = {10.4169/math.mag.88.5.323}, + URL = {https://doi.org/10.4169/math.mag.88.5.323}, +} diff --git a/content/publications.bib b/content/publications.bib deleted file mode 100644 index d6e8d63..0000000 --- a/content/publications.bib +++ /dev/null @@ -1,113 +0,0 @@ -@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.}, - - keywords = {pub}, - journal = {Discrete Mathematics}, - year = {2019}, - month = {Jul.}, - number = {7}, - volume = {342}, - pages = {1865-1884}, -} - -@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.}, - journal = {IEEE Transactions on Information Theory}, - year = {2018}, - keywords = {pub}, -} - -@Article{Cox2018, - author = {Christopher Cox and Derrick Stolee}, - title = {Ramsey Numbers for Partially-Ordered Sets}, - journal = {Order}, - year = {2018}, - month = {Nov.}, - keywords = {pub}, - volume = {35}, - number = {3}, - pages = {557-579}, -} - -@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 = {Jul.}, - keywords = {pub}, - owner = {Chris}, - timestamp = {2015.08.05}, - url = {http://arxiv.org/abs/1512.03787}, -} - -@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 = {Mar.}, - 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 = {Sep.}, - keywords = {pub}, - owner = {Chris}, - url = {http://arxiv.org/abs/1508.05296} -} -@Article{CS16orram, - Title = {Ordered {R}amsey numbers of loose paths and matchings}, - Author = {Cox, Christopher and Stolee, Derrick}, - Journal = {Discrete Mathematics}, - Year = {2016}, - Month = {Feb.}, - 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{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 = {Dec.}, - 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}, -} diff --git a/content/submitted.bib b/content/submitted.bib deleted file mode 100644 index 39b698d..0000000 --- a/content/submitted.bib +++ /dev/null @@ -1,11 +0,0 @@ -@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}, -} |