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Cats in cubes
Noga Alon, Noah Kravitz
Answering a recent question of Patchell and Spiro, we show that when a -dimensional cube of side length is filled with letters, the word can appear contiguous…
The runsort permuton
Noga Alon, Colin Defant, Noah Kravitz
Suppose we choose a permutation uniformly at random from . Let be the permutation obtained by sorting the ascending runs of into lexicographic or…
Inverse problems for minimal complements and maximal supplements
Noga Alon, Noah Kravitz, Matt Larson
Given a subset of an abelian group , a subset is called an additive complement for if ; if, moreover, no proper subset of has this property, then we say t…
Promotion Sorting
Colin Defant, Noah Kravitz
Schützenberger's promotion operator is an extensively-studied bijection that permutes the linear extensions of a finite poset. We introduce a natural extension of this o…
Supertrees
Colin Defant, Noah Kravitz, Ashwin Sah
A -universal permutation, or -superpermutation, is a permutation that contains all permutations of length as patterns. The problem of finding the minimum length of a -…
Stack-sorting for Words
Colin Defant, Noah Kravitz
We introduce operators and , which act on words as natural generalizations of West's stack-sorting map. We show that the heuristically slower alg…