Proof of a conjecture on the slit plane problem
نویسنده
چکیده
Let ai,j(n) denote the number of walks in n steps from (0, 0) to (i, j), with steps (±1, 0) and (0,±1), never touching a point (−k, 0) with k ≥ 0 after the starting point. Bousquet-Mélou and Schaeffer conjectured a closed form for the number a −i,i(2n) when i ≥ 1. In this paper, we prove their conjecture, and give a formula for a −i,i(2n) for i ≤ −1.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 282 شماره
صفحات -
تاریخ انتشار 2004