A refined sign-balance of simsun permutations

Sen-Peng Eu, Tung Shan Fu, Yeh Jong Pan

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4 Citations (Scopus)

Abstract

We present a refined sign-balance result for simsun permutations. On the basis of our previously established bijection between simsun permutations and increasing 1-2 trees, we deduce the recurrence relation and exponential generating function for the sign-balance of simsun permutations of length n with k descents. For odd lengths, the distribution turns out to be (shifted) second-order Eulerian numbers. For even lengths, the distribution forms a signed triangle whose row sums are all zeros. Meanwhile, we obtain two Pólya frequency sequences, one of which refines the double factorial of the odd numbers and the other, that of the even numbers.

Original languageEnglish
Pages (from-to)97-109
Number of pages13
JournalEuropean Journal of Combinatorics
Volume36
DOIs
Publication statusPublished - 2014 Feb 1

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ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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