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Results tagged with co.combinatorics
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user 2641
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
3
votes
Accepted
Making a non-monotone function monotone
A combinatorial proof was found last year by Chakrabarty and Seshadhri: http://eccc.hpi-web.de/report/2012/030/download. In Theorem 3 they show that indeed $E(f) = \Omega(M(f))$.
15
votes
1
answer
1k
views
Making a non-monotone function monotone
Consider a function $f: \{0,1\}^n \rightarrow \{1..R\}$. This function can be interpreted as a coloring $Color(v)$ of vertices in a unit n-dimensional hypercube in $R$ colors.
We say there is a dire …
11
votes
1
answer
1k
views
Maximum number of perfect matchings in a graph
What is the maximal number of perfect matchings a graph $G(V,E)$ can have if $|V|$ and $|E|$ are fixed? I am particularly interested in a case when $|E| = c|V|^2$.
- 17k