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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

5 votes
0 answers
129 views

Random process on a sequence of rolls of an $n$-sided die

Let $\ X:=X_{k\,n}\ $ be a random variable of a $n$-sided die where $\Pr(X=i)=\frac{1}{n}$ for each $i\in\{1,2,\ldots,n\},\ $ where $\ k\in\{1, 2, \ldots,n\}\ $ and $\ n\ $ are fixed. Let $t$ be a par …
2 votes
0 answers
163 views

Finding an optimal strategy for a combinatorial sequential game

We are given a set $\{p_1, p_2, \ldots, p_n\}$ of players and a set of $\{\ell_1, \ell_2, \ldots, \ell_n\}$ of locations, where $n\in\mathbb{N}$. Each location can be either free or occupied, and each …