@unpublished{briggs_frogs, title = {Frogs, hats and common subsequences}, author = {Briggs, Joseph and Parker, Alex and Schwieder, Coy}, month = {apr}, year = {2024}, eprint = {2404.07285}, eprinttype = {arXiv}, eprintclass = {math.CO}, <<<<<<< HEAD keywords = {accepted}, journal = {Electronic Journal of Probability}, ||||||| parent of d4fa2ae (Updated papers) keywords = {submitted}, ======= keywords = {accepted}, journal = {Electronic Journal of Probability}, >>>>>>> d4fa2ae (Updated papers) author+an = {2=earlygrad; 3=earlygrad}, } @unpublished{briggs_phases, author = {Briggs, Joseph}, title = {Phase transitions in isoperimetric problems on the integers}, year = {2024}, month = {feb}, eprint = {2402.14087}, eprintclass = {math.CO}, eprinttype = {arxiv}, keywords = {accepted}, journal = {Discrete Mathematics} } @article{briggs_vietoris, author = {Briggs, Joseph and Feng, Ziqin}, doi = {10.1080/10586458.2025.2474034}, journal = {Experimental Mathematics}, month = {3}, pages = {1--9}, publisher = {Informa UK Limited}, title = {Facets in the {V}ietoris\textendash{}{R}ips Complexes of Hypercubes}, year = {2025}, keywords = {published}, eprint = {2408.01288}, eprinttype = {arXiv}, eprintclass = {math.AT}, } @article{heath_oddcycles, author = {Heath, Emily and Martin, Ryan R.}, doi = {10.1002/jgt.23197}, journal = {Journal of Graph Theory}, month = {4}, pages = {745--780}, publisher = {Wiley}, title = {The maximum number of odd cycles in a planar graph}, volume = {108}, year = {2025}, keywords = {published}, eprint = {2307.00116}, eprintclass = {math.CO}, eprinttype = {arxiv}, % issue = {4}, } @article{sipp, author = {Brennan, Zach and Curtis, Bryan and Gomez-Leos, Enrique and Hadaway, Kimberly and Hogben, Leslie and Thompson, Conor}, title = {Orthogonal realizations of random sign patterns and other applications of the SIPP}, journal = {Electronic Journal of Linear Algebra}, volume = {39}, pages = {434--459}, year = {2023}, month = {aug}, doi = {10.13001/ela.2023.7579}, eprint = {2212.05207}, eprintclass = {math.CO}, eprinttype = {arxiv}, keywords = {published}, author+an = {1=earlygrad; 3=earlygrad; 4=earlygrad; 6=earlygrad}, abstract = {A sign pattern is an array with entries in $\{+,-,0\}$. A matrix $Q$ is row orthogonal if $QQ^T = I$. The Strong Inner Product Property (SIPP), introduced in [B.A.~Curtis and B.L.~Shader, Sign patterns of orthogonal matrices and the strong inner product property, Linear Algebra Appl. 592: 228--259, 2020], is an important tool when determining whether a sign pattern allows row orthogonality because it guarantees there is a nearby matrix with the same property, allowing zero entries to be perturbed to nonzero entries, while preserving the sign of every nonzero entry. This paper uses the SIPP to initiate the study of conditions under which random sign patterns allow row orthogonality with high probability. Building on prior work, $5\times n$ nowhere zero sign patterns that minimally allow orthogonality are determined. Conditions on zero entries in a sign pattern are established that guarantee any row orthogonal matrix with such a sign pattern has the SIPP.} } @article{cox_planarcycles, author = {Martin, Ryan R.}, title = {The maximum number of 10- and 12-cycles in a planar graph}, year = {2023}, month = {feb}, eprint = {2106.02966}, eprinttype = {arxiv}, eprintclass = {math.CO}, journal = {Discrete Mathematics}, volume = {346}, number = {2}, pages = {113245}, doi = {10.1016/j.disc.2022.113245}, keywords = {published}, } @article{cox_planarpaths, author = {Martin, Ryan R.}, title = {Counting paths, cycles and blow-ups in planar graphs}, journal = {Journal of Graph Theory}, volume = {101}, number = {3}, pages = {521-558}, year = {2022}, month = {apr}, doi = {10.1002/jgt.22838}, eprint = {2101.05911}, eprinttype = {arxiv}, eprintclass = {math.CO}, keywords = {published}, } @article{lcsfrogs, author = {Bukh, Boris}, title = {Periodic words, common subsequences and frogs}, year = {2022}, month = {apr}, journal = {Annals of Applied Probability}, volume = {32}, number = {2}, pages = {1295--1332}, doi = {10.1214/21-AAP1709}, eprint = {1912.03510}, eprintclass = {math.PR}, eprinttype = {arxiv}, extra = {Code}, keywords = {published}, } @article{cox_editdistance, author = {Martin, Ryan R. and McGinnis, Daniel}, title = {Accumulation points of the edit distance function}, year = {2022}, month = {jul}, journal = {Discrete Mathematics}, volume = {345}, number = {7}, pages = {112857}, eprint = {2107.06706}, eprinttype = {arxiv}, eprintclass = {math.CO}, doi = {10.1016/j.disc.2022.112857}, keywords = {published}, author+an = {2=earlygrad}, } @article{onlineramsey, author = {Briggs, Joseph}, title = {Restricted online Ramsey numbers of matchings and trees}, journal = {Electronic Journal of Combinatorics}, year = {2020}, month = {sep}, eprint = {1904.00246}, eprintclass = {math.CO}, eprinttype = {arxiv}, doi = {10.37236/8649}, keywords = {published}, abstract = {Consider a two-player game between players Builder and Painter. Painter begins the game by picking a coloring of the edges of $K_n$, which is hidden from Builder. In each round, Builder points to an edge and Painter reveals its color. Builder's goal is to locate a particular monochromatic structure in Painter's coloring by revealing the color of as few edges as possible. The fewest number of turns required for Builder to win this game is known as the restricted online Ramsey number. In this paper, we consider the situation where this ``particular monochromatic structure'' is a large matching or a large tree. We show that in any $t$-coloring of $E(K_n)$, Builder can locate a monochromatic matching on at least ${n-t+1\over t+1}$ edges by revealing at most $O(n\log t)$ edges. We show also that in any $3$-coloring of $E(K_n)$, Builder can locate a monochromatic tree on at least $n/2$ vertices by revealing at most $5n$ edges. } } @article{nearorth, author = {Bukh, Boris}, title = {Nearly orthogonal vectors and small antipodal spherical codes}, journal = {Israel Journal of Mathematics}, volume = {238}, year = {2020}, MONTH = {jul}, number = {1}, pages = {359--388}, doi = {10.1007/s11856-020-2027-7}, eprint = {1803.02949}, eprinttype = {arxiv}, eprintclass = {math.CO}, keywords = {published}, } @article{invturan, author = {Briggs, Joseph}, title = {Inverting the Tur{\'a}n problem}, journal = {Discrete Mathematics}, publisher = {Elsevier BV}, year = {2019}, month = {jul}, number = {7}, volume = {342}, pages = {1865--1884}, doi = {10.1016/j.disc.2019.03.005}, eprint = {1711.02082}, eprinttype = {arxiv}, eprintclass = {math.CO}, keywords = {published}, } @article{frachaemers, author = {Bukh, Boris}, title = {On a fractional version of Haemers' bound}, journal = {IEEE Transactions on Information Theory}, publisher = {Institute of Electrical and Electronics Engineers (IEEE)}, year = {2019}, month = {jun}, number = {6}, volume = {65}, pages = {3340--3348}, doi = {10.1109/tit.2018.2889108}, eprint = {1802.00476}, eprinttype = {arxiv}, eprintclass = {cs.IT}, keywords = {published}, } @article{poramsey, author = {Stolee, Derrick}, title = {Ramsey numbers for partially-ordered sets}, journal = {Order}, publisher = {Springer Nature}, year = {2018}, month = {jan}, number = {3}, volume = {35}, pages = {557--579}, doi = {10.1007/s11083-017-9449-9}, eprint = {1512.05261}, eprinttype = {arxiv}, eprintclass = {math.CO}, keywords = {published}, } @article{42choose, author = {Berikkyzy, Zhanar 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 structures}, journal = {Graphs and Combinatorics}, publisher = {Springer Nature}, year = {2017}, month = {jun}, number = {4}, volume = {33}, pages = {751--787}, doi = {10.1007/s00373-017-1812-5}, eprint = {1512.03787}, eprinttype = {arxiv}, eprintclass = {math.CO}, keywords = {published}, abstract = {All planar graphs are $4$-colorable and $5$-choosable, while some planar graphs are not $4$-choosable. Determining which properties guarantee that a planar graph can be colored using lists of size four has received significant attention. In terms of constraining the structure of the graph, for any $\ell\in\{3,4,5,6,7\}$, a planar graph is $4$-choosable if it is $\ell$-cycle-free. In terms of constraining the list assignment, one refinement of $k$-choosability is choosability with separation. A graph is $(k, s)$-choosable if the graph is colorable from lists of size $k$ where adjacent vertices have at most $s$ common colors in their lists. Every planar graph is $(4, 1)$-choosable, but there exist planar graphs that are not $(4, 3)$-choosable. It is an open question whether planar graphs are always $(4, 2)$-choosable. A chorded $\ell$-cycle is an $\ell$-cycle with one additional edge. We demonstrate for each $\ell\in\{5,6,7\}$ that a planar graph is $(4, 2)$-choosable if it does not contain chorded $\ell$-cycles. } } @article{eulerrooks, author = {Banaian, Esther and Butler, Steve and Davis, Jeffrey and Landgraf, Jacob and Ponce, Scarlitte}, title = {A generalization of Eulerian numbers via rook placements}, journal = {Involve, a Journal of Mathematics}, publisher = {Mathematical Sciences Publishers}, year = {2017}, month = {mar}, number = {4}, volume = {10}, pages = {691--705}, doi = {10.2140/involve.2017.10.691}, eprint = {1508.03673}, eprinttype = {arxiv}, eprintclass = {math.CO}, keywords = {published}, author+an = {1=undergrad; 3=undergrad; 4=undergrad; 5=undergrad}, } @article{primejuggle, author = {Banaian, Esther and Butler, Steve and Davis, Jeffrey and Landgraf, Jacob and Ponce, Scarlitte}, title = {Counting prime juggling patterns}, journal = {Graphs and Combinatorics}, publisher = {Springer Science and Business Media LLC}, year = {2016}, month = {may}, number = {5}, volume = {32}, pages = {1675--1688}, doi = {10.1007/s00373-016-1711-1}, eprint = {1508.05296}, eprinttype = {arxiv}, eprintclass = {math.CO}, keywords = {published}, author+an = {1=undergrad; 3=undergrad; 4=undergrad; 5=undergrad}, } @article{loosepath, author = {Stolee, Derrick}, title = {Ordered Ramsey numbers of loose paths and matchings}, journal = {Discrete Mathematics}, publisher = {Elsevier BV}, year = {2016}, month = {feb}, number = {2}, volume = {339}, pages = {499--505}, doi = {10.1016/j.disc.2015.09.026}, eprint = {1411.4058}, eprinttype = {arxiv}, eprintclass = {math.CO}, keywords = {published}, abstract = {For a $k$-uniform hypergraph $G$ with vertex set $\{1,\dots,n\}$, the ordered Ramsey number $\operatorname{OR}_t(G)$ is the least integer $N$ such that every $t$-coloring of the edges of the complete $k$-uniform graph on vertex set $\{1,\dots,N\}$ 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 et al. (2015) 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. } } @article{hanabi, author = {De Silva, Jessica and DeOrsey, Philip and Kenter, Franklin and Retter, Troy and Tobin, Josh}, title = {How to make the perfect fireworks display: Two strategies for \emph{Hanabi}}, journal = {Mathematics Magazine}, publisher = {Informa UK Limited}, year = {2015}, month = {dec}, number = {5}, volume = {88}, pages = {323--336}, doi = {10.4169/math.mag.88.5.323}, keywords = {published}, }