A note on statistical averages for oscillating tableaux
Name
Hopkins-2015-Note on statistical.pdf
Size
255.79 KB
Format
Adobe PDF
Checksum (MD5)
44fe50570a73e88ea88adfa5b2e8c893
Author(s)
Hopkins, Samuel Francis
Zhang, Ingrid
Date Issued
June 2015
Journal
Electronic Journal of Combinatorics
Publisher
European Mathematical Information Service (EMIS)
Citation
Hopkins, Sam, and Ingrid Zhang. "A note on statistical averages for oscillating tableaux." The Electronic Journal of Combinatorics 22(2) (2015), #P2.48.
Version
Final published version
Abstract
Oscillating tableaux are certain walks in Young's lattice of partitions; they generalize standard Young tableaux. The shape of an oscillating tableau is the last partition it visits and the length of an oscillating tableau is the number of steps it takes. We define a new statistic for oscillating tableaux that we call weight: the weight of an oscillating tableau is the sum of the sizes of all the partitions that it visits. We show that the average weight of all oscillating tableaux of shape λ and length |λ| + 2n (where |λ| denotes the size of λ and n ∈ N) has a surprisingly simple formula: it is a quadratic polynomial in |λ| and n. Our proof via the theory of differential posets is largely computational. We suggest how the homomesy paradigm of Propp and Roby may lead to a more conceptual proof of this result and reveal a hidden symmetry in the set of perfect matchings.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.37236/4641
