کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1148377 | 957831 | 2014 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Lattice and Schröder paths with periodic boundaries
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
We consider paths in the plane with (1,0), (0,1), and (a,b)-steps that start at the origin, end at height n, and stay strictly to the left of a given non-decreasing right boundary. We show that if the boundary is periodic and has slope at most b/a, then the ordinary generating function for the number of such paths ending at height n is algebraic. Our argument is in two parts. We use a simple combinatorial decomposition to obtain an Appell relation or “umbral” generating function, in which the power zn is replaced by a power series of the form znÏn(z), where Ïn(0)=1. Then we convert (in an explicit way) the umbral generating function to an ordinary generating function by solving a system of linear equations and a polynomial equation. This conversion implies that the ordinary generating function is algebraic. We give several concrete examples, including an alternative way to solve the tennis ball problem.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Statistical Planning and Inference - Volume 139, Issue 6, 1 June 2009, Pages 2014-2027
Journal: Journal of Statistical Planning and Inference - Volume 139, Issue 6, 1 June 2009, Pages 2014-2027
نویسندگان
Joseph P.S. Kung, Anna de Mier, Xinyu Sun, Catherine Yan,