کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1150110 957913 2011 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On three and four vicious walkers
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
On three and four vicious walkers
چکیده انگلیسی

We establish a reflection principle for three lattice walkers and use this principle to reduce the enumeration of configurations of three vicious walkers to the enumeration of configurations of two vicious walkers. More precisely, the reflection principle leads to a bijection between three walks (L1, L2, L3) such that L2 intersects both L1 and L3 and three walks (L1, L2, L3) such that L1 intersects L3. Hence we find a combinatorial interpretation of the formula for the generating function for the number of configurations of three vicious walkers, originally derived by Bousquet-Mélou by using the kernel method, and independently by Gessel by using tableaux and symmetric functions. This answers a question posed by Gessel and Bousquet-Mélou. We also find a reflection principle for four vicious walks that leads to a combinatorial interpretation of a formula derived from Gessel's theorem.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Statistical Planning and Inference - Volume 141, Issue 1, January 2011, Pages 94–101
نویسندگان
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