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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.

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1 answer
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ask for a simple bijective proof about oriented increasing binary trees

Give a bijective proof-----the number of oriented increasing binary trees on the vertex set $\lbrace 1,2,\cdots,n\rbrace$ is the Eulerian number $E_n$(the number of alternating permutations in $\math …
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4 votes
1 answer
547 views

a simple combinatorial problems

what sequence $C=(c_1,\cdots,c_n)\in \mathbb{N}^n$ with $\sum ic_i=n$ maximizes the number of $\omega\in\mathfrak{S}_n$ of type $C$? For instance,when $n=4$ the maximizing sequence is $(1,0,1,0)$.
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