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Two other interpretations of the Entringer numbers. (English) Zbl 0886.05011

Author’s summary: The Entringer’s integers were introduced to enumerate the down-up (or up-down) permutation according to the first term. In a previous paper these integers are shown to enumerate André’s trees according to two parameters. In this paper we prove that they enumerate the direct alternative permutations according to the absolute value of the first two terms and also according to a specified term.

MSC:

05A15 Exact enumeration problems, generating functions
05A05 Permutations, words, matrices
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