# 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.

6,390 questions
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### Bijective operations on finite simple graphs

Let $\mathcal G_n$ be the set of (isomorphism classes of unlabelled) simple graphs on $n$ vertices. I am interested in specific bijective maps $\mathcal G_n\to\mathcal G_n$, defined for all $n$. An ...
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### Is the Ford-Fulkerson algorithm a tropical rational function?

The Ford-Fulkerson algorithm Let me recall the standard scenario of flow optimization (for integer flows at least): Let $\mathbb{N} = \left\{0,1,2,\ldots\right\}$. Consider a digraph $D$ with vertex ...
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### Sum of Binomial Coefficients from 1 to N having specific form [on hold]

In this question I want to know how we can find the sum of the series if N = 2*I like 2C1 + 4C2 + 6C3 + …. upto N terms. [Sum of 'the first k' binomial coefficients for fixed n
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### Maximum determinant of $\{0,1\}$-valued $n\times n$-matrices

What's the maximum determinant of $\{0,1\}$ matrices in $M(n,\mathbb{R})$? If there's no exact formula what are the nearest upper and lower bounds do you know?
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### Transforming a binary matrix into triangular form using permutation matrices

I am interested in the complexity of the following problem: Given an $m\times n$ binary matrix $M$, can we permute its rows/columns to obtain a triangular matrix? I am also interested in ...
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### What kind of curve is this, from the distribution of roots of Catalan polynomials? [closed]

We consider the distribution of roots of some Catalan polynomials. And we get the following curve that the roots approach it. What kind of curve is this?
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### Combinatorial inequality for dominant dimension

In the following I present a conjecture on Nakayama algebras that I have for nearly 2 years now. Since I was not able to solve it and it can be stated purely combinatorically, I thought it might be ...
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### On the “infinitely often in” relation between subsets of $\mathbb{N}$

Let ${\mathbb N}$ denote the set of positive integers, let $A,B\subseteq \mathbb{N}$. For $n\in\mathbb{N}$ we set $n+A:=\{n+a: a\in A\}$. We say that $A$ is infinitely often in $B$ if the set \big\{...
### Finding $P$ points among $N$ to approximate a probability density function?
Let $f$ be a probability density function (positive such that $\int_{\mathbb{R}} f(x) \mathrm{d} x = 1$) and $X_0 = \{x_n\}_{1\leq n \leq N}$ be $N$ given real points. We also fix $1 \leq P \leq N$ ...