A refined sign-balance of simsun permutations

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

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

6 引文 斯高帕斯(Scopus)

摘要

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.

原文英語
頁(從 - 到)97-109
頁數13
期刊European Journal of Combinatorics
36
DOIs
出版狀態已發佈 - 2014 二月

ASJC Scopus subject areas

  • 離散數學和組合

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