625 citations
- California Institute of TechnologyUS82 papers
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12 papers · 1 filter
Leaky Positive Semidefinite Forcing on Graphs
Olivia Elias, Ian Farish, Emrys King +2
We introduce -leaky positive semidefinite forcing and the -leaky positive semidefinite number of a graph, , which combines the positive semidefinite co…
Probabilistic chip-collecting games with modulo winning conditions
Joshua Harrington, Xuwen Hua, Xufei Liu +3
Let , , and be integers with . In a certain two-player probabilistic chip-collecting game, Alice tosses a coin to determine whether she collects chips or …
Avoiding Brooms, Forks, and Butterflies in the Linear Lattices
Shahriar Shahriari, Song Yu
Let be a positive integer, a power of a prime, and the poset of subspaces of an -dimensional vector space over a field with elements. This poset i…
Asymptotic distribution of fixed points of pattern-avoiding involutions
Samuel Miner, Douglas Rizzolo, Erik Slivken
For a variety of pattern-avoiding classes, we describe the limiting distribution for the number of fixed points for involutions chosen uniformly at random from that class. In parti…
Proving Tucker's Lemma with a Volume Argument
Beauttie Kuture, Oscar Leong, Christopher Loa +2
Sperner's lemma is a statement about labeled triangulations of a simplex. McLennan and Tourky (2007) provided a novel proof of Sperner's Lemma by examining volumes of simplices in…
Permutation invariant lattices
Lenny Fukshansky, Stephan Ramon Garcia, Xun Sun
We say that a Euclidean lattice in is permutation invariant if its automorphism group has non-trivial intersection with the symmetric group , i.e., if the lattic…