Questions tagged [co.combinatorics]

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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19
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5answers
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Cauchy-Schwarz and pigeonhole

I've occasionally heard it stated (most notably on Terry Tao's blog) that "the Cauchy-Schwarz inequality can be viewed as a quantitative strengthening of the pigeonhole principle." I've certainly seen ...
3
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2answers
745 views

Is the “diagonal” of a regular language always context-free?

That's very poor wording, so let me be more precise. Suppose $L$ is an unambiguous regular language on an alphabet $\{a_1, \dots, a_n\}$, and suppose to each letter of the alphabet we associate two ...
6
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1answer
1k views

Specializations of Schur functions at consecutive integers

Given a partition λ = (λ1, λ2, ..., λn) denote with sλ the associated Schur function. There exists a nice product formula for the principal specializations: sλ...
5
votes
3answers
971 views

What is the expected number of maximal bicliques in a random bipartite graph?

Maximal Biclique: A complete bipartite subgraph, that isn't a subgraph of another complete bipartite subgraph. Given a bipartite graph $G=(V_{1}\cup V_{2}, E)$ where $|V_{1}|=|V_{2}|$ with ...
13
votes
1answer
616 views

What are the Schur functions of the eigenvalues of a non-negative integer matrix counting?

Let A be a non-negative integer square matrix with eigenvalues x1, x2, ... xn. Any symmetric function of these eigenvalues with integer matrices is an integer. I'm aware of the following results ...
7
votes
2answers
779 views

Finding monochromatic rectangles in a countable coloring of $R^{2}$

Given a countable coloring of the plane, is it always possible to find a monochromatic set of points $\left\{ \left(x,y\right),\left(x+w,y\right),\left(x,y+h\right),\left(x+w,y+h\right)\right\} $ (the ...
0
votes
0answers
1k views

Ignore this question [closed]

This question is a hacky way to create some tags for you to use. Move along.

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