Fixed points of the evacuation of maximal chains on fuss shapes

Sen Peng Eu, Tung Shan Fu, Hsiang Chun Hsu, Yu Pei Huang

研究成果: 雜誌貢獻期刊論文同行評審

摘要

For a partition λ of an integer, we associate λ with a slender poset P the Hasse diagram of which resembles the Ferrers diagram of λ. Let X be the set of maximal chains of P. We consider Stanley’s involution ɛ: X → X, which is extended from Schützenberger’s evacuation on linear extensions of a finite poset. We present an explicit characterization of the fixed points of the map ɛ: X → X when λ is a stretched staircase or a rectangular shape. Unexpectedly, the fixed points have a nice structure, i.e., a fixed point can be decomposed in half into two chains such that the first half and the second half are the evacuation of each other. As a consequence, we prove anew Stembridge’s q = −1 phenomenon for the maximal chains of P under the involution ɛ for the restricted shapes.

原文英語
期刊Electronic Journal of Combinatorics
25
發行號1
DOIs
出版狀態已發佈 - 2018 二月 16

ASJC Scopus subject areas

  • 理論電腦科學
  • 幾何和拓撲
  • 離散數學和組合
  • 計算機理論與數學
  • 應用數學

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