A Survey of Alternating Permutations

Richard P. Stanley

A Survey of Alternating Permutations

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arxiv 0912.4240 v1 pith:L5PTOLJU submitted 2009-12-21 math.CO

Richard P. Stanley This is my paper · ORCID

classification math.CO

keywords alternatingeulernumberspermutationssurveycd-indexclassesenumeration

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This survey of alternating permutations and Euler numbers includes refinements of Euler numbers, other occurrences of Euler numbers, longest alternating subsequences, umbral enumeration of classes of alternating permutations, and the cd-index of the symmetric group.

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Combinatorial interpretation of the coefficients of the order polynomial of fence posets
math.CO 2026-07 accept novelty 7.0 of 10

The statistic bl_P on permutations equals the coefficients of the order polynomial of a fence poset P, and extends to Ehrhart polynomials of Schubert matroid base polytopes.

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