For questions about the study of finite or countable discrete structures, specifically how to count or enumerate elements in a set (perhaps of all possibilities) or any subset. It includes questions on permutations, combinations, bijective proofs, and generating functions.

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5
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0answers
138 views
+50

The recurrence $a_k(n) = \sum_{0\leqslant j<n} a_{k-1}(n+j)$

I'm trying to find a closed form expression to the following recurrence relation: \begin{align} &a_k(0) = 0, \quad \forall k\geqslant 1; \\ &a_k(1) = 1, \quad \forall k\geqslant 1; \\ ...
2
votes
1answer
104 views
+50

Result of a $2D$ random walk with position dependent probabilities

I was just wondering about $2D$ random walks when I got the idea of a position dependent $2D$ random walk: A man is initially at $(x,y)$ and can move in a line parallel to the X and Y-axis only. ...