On Enumeration of Families of Genus Zero Permutations

Sen Peng Eu, Tung Shan Fu, Yeh Jong Pan, Chien Tai Ting*

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

摘要

The genus of a permutation σ of length n is the nonnegative integer gσ given by n+ 1 - 2 gσ= cyc(σ) + cyc(σ- 1ζn) , where cyc(σ) is the number of cycles of σ and ζn is the cyclic permutation (1 , 2 , … , n). On the basis of a connection between genus zero permutations and noncrossing partitions, we enumerate the genus zero permutations with various restrictions, including André permutations, simsun permutations, and smooth permutations. Moreover, we present refined sign-balance results on genus zero permutations and their analogues restricted to connected permutations.

原文英語
頁(從 - 到)1337-1360
頁數24
期刊Graphs and Combinatorics
35
發行號6
DOIs
出版狀態已發佈 - 2019 十一月 1

ASJC Scopus subject areas

  • 理論電腦科學
  • 離散數學和組合

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