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• W2887229251 abstract "Johnson proved that if s , t are coprime integers, then the r th moment of the size of an ( s , t ) -core is a polynomial of degree 2 r in t for fixed s . After that, by defining a statistic size on elements of affine Weyl group, which is preserved under the bijection between minimal coset representatives of S ˜ t ∕ S t and t -cores, Thiel and Williams obtained the variance and the third moment about the mean of the size of an ( s , t ) -core. Later, Ekhad and Zeilberger stated the first six moments about the mean of the size of an ( s , t ) -core and the first nine moments about the mean of the size of an ( s , s + 1 ) -core using Maple. To get the moments about the mean of the size of a self-conjugate ( s , t ) -core, we proceed to follow the approach of Thiel and Williams, however, their approach does not seem to directly apply to the self-conjugate case. In this paper, following Johnson’s approach, by Ehrhart theory and Euler–Maclaurin theory, we prove that if s , t are coprime integers, then the r th moment about the mean of the size of a self-conjugate ( s , t ) -core is a quasipolynomial of period 2 and degree 2 r in t for fixed odd s . Then, based on a bijection of Ford, Mai and Sze between self-conjugate ( s , t ) -cores and lattice paths in s 2 × t 2 rectangle and a formula of Chen, Huang and Wang on the size of self-conjugate ( s , t ) -cores, we obtain the variance, the third moment and the fourth moment about the mean of the size of a self-conjugate ( s , t ) -core." @default.
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• W2887229251 date "2018-11-01" @default.
• W2887229251 modified "2023-09-29" @default.
• W2887229251 title "Moments about the mean of the size of a self-conjugate <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=mml4 display=inline overflow=scroll altimg=si4.gif><mml:mrow><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>-core partition" @default.
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• W2887229251 doi "https://doi.org/10.1016/j.disc.2018.07.006" @default.
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