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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.

4 votes
1 answer
382 views

Turan numbers of r-partite hypergraphs

Let $H$ be a balanced $r$-partite $r$-uniform hypergraph with $nr$ vertices. (Each part of this hypergraph consists of $n$ vertices; every hyperedge has exactly one vertex in each part.) Denote a comp …
6 votes
1 answer
3k views

Mathematical expectation of minimum of k random variables with fixed sum n

We have $n$ independent identically distributed random variables $X_1$, $X_2$, ..., $X_N$, $X_i=j$ with probability $1/k$ for $j=1, 2, ... k$. Let $Y_j$ be a number of random variables $X_i$, which ar …