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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/115407

    Title: Fixed points of the evacuation of maximal chains on Fuss shapes
    Authors: Sen-Peng Eu;Tung-Shan Fu;Hsiang-Chun Hsu;Yu-Pei Huang
    Keywords: Evacuation;Stembridge's q=-1 phenomenon;Fixed point;Partition
    Date: 2018-02-28
    Issue Date: 2018-10-25 12:11:01 (UTC+8)
    Abstract: 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 ϵ: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
    ϵ: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=−1phenomenon for the maximal chains of P under the involution ϵ for the restricted shapes.
    Relation: The Electronic Journal of Combinatorics 25(1), p1-33
    Appears in Collections:[Graduate Institute & Department of Mathematics] Journal Article

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