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Descent c-Wilf Equivalence
Bach, Quang T....

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Descent c-Wilf Equivalence by Bach, Quang T. ( Author )
Lemonjar Open Access
N.A
24-10-2015
Let Sn denote the symmetric group. For any σ∈Sn, we let des(σ) denote the number of descents of σ, inv(σ) denote the number of inversions of σ, and LRmin(σ) denote the number of left-to-right minima of σ. For any sequence of statistics stat1,…statk on permutations, we say two permutations α and β in Sj are (stat1,…statk)-c-Wilf equivalent if the generating function of ∏ki=1xstatii over all permutations which have no consecutive occurrences of α equals the generating function of ∏ki=1xstatii over all permutations which have no consecutive occurrences of β. We give many examples of pairs of permutations α and β in Sj which are des-c-Wilf equivalent, (des,inv)-c-Wilf equivalent, and (des,inv,LRmin)-c-Wilf equivalent. For example, we will show that if α and β are minimally overlapping permutations in Sj which start with 1 and end with the same element and des(α)=des(β) and inv(α)=inv(β), then α and β are (des,inv)-c-Wilf equivalent.
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Article
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36.88 KB
English
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MYR 0.01
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https://arxiv.org/abs/1510.07190
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