کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8902825 | 1632393 | 2018 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Moments about the mean of the size of a self-conjugate (s,t)-core partition
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Johnson proved that if s,t are coprime integers, then the rth moment of the size of an (s,t)-core is a polynomial of degree 2r 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 SËtâSt 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 rth moment about the mean of the size of a self-conjugate (s,t)-core is a quasipolynomial of period 2 and degree 2r 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 s2Ãt2 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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 341, Issue 11, November 2018, Pages 3029-3043
Journal: Discrete Mathematics - Volume 341, Issue 11, November 2018, Pages 3029-3043
نویسندگان
Joseph L.P. Wang, Larry X.W. Wang, Jane Y.X. Yang,