Priority Queue Sorting and Labeled Trees

Hamel, Angèle M.

doi:10.1007/s000260300004

Cited by 2 publications

(2 citation statements)

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“…Using Theorem 4.9, we conclude that the number of allowable pairs (σ 1 , σ 2 ) with σ 1 , σ 2 ∈ S n is (n + 1) n−1 . Of course, this fact was proved before [3,4,22] but our proof is different from the aforementioned ones.…”

Section: Allowable Pairs Of Permutations and Acyclic Graphsmentioning

confidence: 52%

“…Section 5 gives a characterization for compatible pairs in terms of pattern-avoidance. We demonstrate that compatible pairs are essentially allowable pairs introduced in [4] and investigated further in [3,18,22]. To answer our original question, we show in Corollary 5.8 that every allowable pair can be obtained by standardizing the entries in the last two columns of some standard composition tableau.…”

Section: Introductionmentioning

confidence: 88%

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Permuted composition tableaux, 0-Hecke algebra and labeled binary trees

Tewari

Willigenburg

2019

Journal of Combinatorial Theory, Series A

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We introduce a generalization of semistandard composition tableaux called permuted composition tableaux. These tableaux are intimately related to permuted basement semistandard augmented fillings studied by Haglund, Mason and Remmel. Our primary motivation for studying permuted composition tableaux is to enumerate all possible ordered pairs of permutations (σ 1 , σ 2 ) that can be obtained by standardizing the entries in two adjacent columns of an arbitrary composition tableau. We refer to such pairs as compatible pairs. To study compatible pairs in depth, we define a 0-Hecke action on permuted composition tableaux. This action naturally defines an equivalence relation on these tableaux. Certain distinguished representatives of the resulting equivalence classes in the special case of two-columned tableaux are in bijection with compatible pairs. We provide a bijection between two-columned tableaux and labeled binary trees. This bijection maps a quadruple of descent statistics for 2-columned tableaux to left and right ascent-descent statistics on labeled binary trees introduced by Gessel, and we use it to prove that the number of compatible pairs is (n + 1) n−1 . 14 4.2. Bijection between LD n and SPCT((2 n )) 15 4.3. Plane binary trees, unlabeled and labeled 162010 Mathematics Subject Classification. Primary 05E10, 20C08; Secondary 05A05, 05A19, 05C20, 05E05, 05E15.

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Section: Allowable Pairs Of Permutations and Acyclic Graphsmentioning

confidence: 52%