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Flip-sort and combinatorial aspects of pop-stack sorting [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 Flip-sort is a natural sorting procedure which raises fascinating combinatorial questions. It finds its roots in the seminal work of Knuth on stack-based sorting algorithms and leads to many links with permutation patterns. We present several structural,
Andrei Asinowski +2 more
doaj +8 more sources
Pop-stack-sorting for Coxeter groups [PDF]
Combinatorial Theory, 2022 24 pages, 7 figures, to be published in Combinatorial ...
Colin Defant
exaly +9 more sources
Enumeration of Stack-Sorting Preimages via a Decomposition Lemma [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 We give three applications of a recently-proven "Decomposition Lemma," which allows one to count preimages of certain sets of permutations under West's stack-sorting map $s$.
Colin Defant
doaj +7 more sources
Troupes, cumulants, and stack-sorting [PDF]
Advances in Mathematics, 2022 Several sequences of free cumulants that count binary plane trees correspond to sequences of classical cumulants that count the decreasing versions of the same trees. Using two new operations on colored binary plane trees that we call insertion and decomposition, we prove that this surprising phenomenon holds for families of trees that we call troupes.
Colin Defant
exaly +4 more sources
Deterministic stack-sorting for set partitions
Enumerative Combinatorics and Applications, 2023 A sock sequence is a sequence of elements, which we will refer to as socks, from a finite alphabet. A sock sequence is sorted if all occurrences of a sock appear consecutively. We define equivalence classes of sock sequences called sock patterns, which are in bijection with set partitions.
Janabel Xia
doaj +3 more sources
2-Stack Sorting is Polynomial [PDF]
Theory of Computing Systems, 2017 23 ...
Dominique Rossin
exaly +8 more sources
Stack-sorting with consecutive-pattern-avoiding stacks [PDF]
Advances in Applied Mathematics, 2021 We introduce consecutive-pattern-avoiding stack-sorting maps $\text{SC}_σ$, which are natural generalizations of West's stack-sorting map $s$ and natural analogues of the classical-pattern-avoiding stack-sorting maps $s_σ$ recently introduced by Cerbai, Claesson, and Ferrari.
Colin Defant
exaly +4 more sources
Preimages Under the Stack-Sorting Algorithm [PDF]
Graphs and Combinatorics, 2016 We use a method for determining the number of preimages of any permutation under the stack-sorting map in order to obtain recursive upper bounds for the numbers $W_t(n)$ and $W_t(n,k)$ of $t$-stack sortable permutations of length $n$ and $t$-stack sortable permutations of length $n$ with exactly $k$ descents.
Colin Defant
exaly +3 more sources
Crystal pop-stack sorting and type A crystal lattices [PDF]
European Journal of Combinatorics, 2022 16 pages, 4 ...
Colin Defant
exaly +5 more sources
Stack-sorting, set partitions, and Lassalle's sequence
Journal of Combinatorial Theory - Series A, 2020 We exhibit a bijection between recently-introduced combinatorial objects known as valid hook configurations and certain weighted set partitions. When restricting our attention to set partitions that are matchings, we obtain three new combinatorial interpretations of Lassalle's sequence.
Colin Defant, Michael Engen
exaly +5 more sources