کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9506061 | 1340376 | 2005 | 18 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Combinatorics of q,t-parking functions
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In [A conjectured combinatorial formula for the Hilbert series for diagonal harmonics, in: Proceedings of FPSAC 2002 Conference, Melbourne, Australia, Discrete Math., in press] Haglund, Haiman, and the present author conjectured a combinatorial formula CHn(q,t) for the Hilbert series of diagonal harmonics as a weighted sum of parking functions. Another equivalent combinatorial formula was proposed by the present author in [Multivariate analogues of Catalan numbers, parking functions, and their extensions, UCSD doctoral thesis, June 2003]. These formulas involve three statistics on parking functions called area, dinv, and pmaj. In this article, we use the pmaj statistic to solve several combinatorial problems posed in [A conjectured combinatorial formula for the Hilbert series for diagonal harmonics, in: Proceedings of FPSAC 2002 Conference, Melbourne, Australia, Discrete Math., in press]. In particular, we derive a recursion satisfied by the combinatorial Hilbert series and show that qn(nâ1)/2CHn(1/q,q)=[n+1]qnâ1.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Applied Mathematics - Volume 34, Issue 2, February 2005, Pages 408-425
Journal: Advances in Applied Mathematics - Volume 34, Issue 2, February 2005, Pages 408-425
نویسندگان
Nicholas A. Loehr,