Alternating permutations and modified Ghandi-polynomials
V Strehl - Discrete Mathematics, 1979 - Elsevier
V Strehl
Discrete Mathematics, 1979•ElsevierThe presentation of alternating permutatioas via labelled binary trees is used to define
polynomials H 2n− 1 (x) as enumerating polynomials for the height of peaks in alternating
permutations of length 2n− 1. A divisibility property of the coefficients of these polynomials is
proved, which generalizes and explains combinatirially a well-known property of the tangent
numbers. Furthermore, a version of the exponential generating function for the H 2n− 1 (x) is
given, leading to a new combinatorial interpretation of Dumont's modified Ghandi …
polynomials H 2n− 1 (x) as enumerating polynomials for the height of peaks in alternating
permutations of length 2n− 1. A divisibility property of the coefficients of these polynomials is
proved, which generalizes and explains combinatirially a well-known property of the tangent
numbers. Furthermore, a version of the exponential generating function for the H 2n− 1 (x) is
given, leading to a new combinatorial interpretation of Dumont's modified Ghandi …
Abstract
The presentation of alternating permutatioas via labelled binary trees is used to define polynomials H2n−1(x) as enumerating polynomials for the height of peaks in alternating permutations of length 2n−1. A divisibility property of the coefficients of these polynomials is proved, which generalizes and explains combinatirially a well-known property of the tangent numbers. Furthermore, a version of the exponential generating function for the H2n−1(x) is given, leading to a new combinatorial interpretation of Dumont's modified Ghandi-polynomials.
Elsevier
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