# 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.

6,446 questions
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### Consensus clustering using set union

Problem statement Let $P$, $Q$ and $R$ be three partitions into $p$ nonempty parts (denoted by $P_h$'s, $Q_i$'s and $R_j$'s) of the set {$1,2,\ldots,n$}. Find two permutations $\pi$ and $\sigma$ that ...
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### Orthogonal matrices with small entries

Is it true that for any $n$, there exists a $n \times n$ real orthogonal matrix with all coefficients bounded (in absolute value) by $C/\sqrt{n}$, $C$ being an absolute contant ? Some remarks : If ...
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### Erdos Conjecture on arithmetic progressions

Introduction: Let A be a subset of the naturals such that $\sum_{n\in A}\frac{1}{n}=\infty$. The Erdos Conjecture states that A must have arithmetic progressions of arbitrary length. Question: I ...
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### Condition for existence of certain lattice points on polytopes

Let $a_1,\cdots, a_n$ be integers such that $a_i\geq 2$ for all $i$ and $k>0$ another integer. I am interested in whether there exist integers $x_1,\cdots, x_n$ with $0<x_i<a_i$ satisfying: ...
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### How many labelled disconnected simple graphs have n vertices and floor((n choose 2)/2) edges?

I would like to know the asymptotic number of labelled disconnected (simple) graphs with n vertices and $\lfloor \frac 12{n\choose 2}\rfloor$ edges.
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### Weighted Regular Graphs

The following graph theoretic notion appeared in an economics paper entitled: "Prize competition under limited comparability, by Michele Piccione and Ran Spiegler which studies models of economics ...
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### Combinatorial sequences whose ratios $a_{n+1}/a_{n}$ are integers

I have a proof technique in search of examples. I'm looking for combinatorially meaningful sequences $\{a_n\}$ so that $a_{n+1}/a_n$ is known or conjectured to be an integer, such that there is a ...
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### Flipping Hilbert series of semigroup rings

I'll first give intuition, and then give a precise statement. For $|z|<1$, we have $\sum_{i \geq 0} z^i = 1/(1-z)$. For $|z|>1$, we have $\sum_{i<0} (-1) z^i=1/(1-z)$. Thus, the two ...
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### Average distance between numbers of the form $2^{a}3^{b}$

I want to order all numbers of the form $2^a3^b$. I need to find the average distance between a random consecutive pair. For example, in case of a random consecutive pair $2^{n'}$ and $2^{n'+1}$, the ...
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### Combinatorics journals processing time

This is a spin-off question from How to select a journal?. Is there is any data available regarding processing time (acceptance time, time from submission to publication, or similar) specifically for ...
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### Submitting to arXiv when unaffiliated

I am writing a short paper in the area of combinatorics. When the paper is complete, I would like to be able to submit it to arXiv. The reasons that I would like to submit to arXiv are: To obtain a ...
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### Is a lattice of convex sets distributive?

Is a lattice of convex sets in $R^2$ distributive?
### devise a joint distribution of $\alpha$ and $\beta$
If we assume probability density distribution functions of random variables $\alpha$, $\beta$ and $\alpha/ \beta$, we would like to devise a joint distribution of $\alpha$ and $\beta$. Although ...