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Discrete Mathematics & Theoretical Computer Science |
Let gcd(a, b) = 1. J. Olsson and D. Stanton proved that the maximum number of boxes in a simultaneous (a, b)-core is (a2 −1)(b2 −1) 24, and showed that this maximum is achieved by a unique core. P. Johnson combined Ehrhart theory with the polynomial method to prove D. Armstrong's conjecture that the expected number of boxes in a simultaneous (a, b)-core is (a−1)(b−1)(a+b+1) 24. We apply P. Johnson's method to compute the variance and third moment. By extending the definitions of “simultaneous cores” and “number of boxes” to affine Weyl groups, we give uniform generalizations of these formulae to simply-laced affine types. We further explain the appearance of the number 24 using the “strange formula” of H. Freudenthal and H. de Vries.
Source : ScholeXplorer
IsRelatedTo ARXIV 1312.4352 Source : ScholeXplorer IsRelatedTo DOI 10.1137/130950318 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1312.4352
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