# 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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### 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 ...

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### 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 ...

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**1**answer

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### 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**

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### 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**

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**1**answer

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### 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**

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### 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 ...

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**0**answers

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### Ignore this question [closed]

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