# 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.

8,360 questions
Filter by
Sorted by
Tagged with
0answers
124 views

1answer
231 views

0answers
33 views

### Problem concerning cutting of 2n*2n square into 2 equal area connected figures using various cuts without self crossings

We have a square 2n*2n, where n belongs to N. The main problem is to find how many different equal area connected figures could be produced by cuttings without self-crossings. The orientability of the ...
2answers
519 views

### Alternating sum of hook lengths: Part I

Given $\lambda$ an integer partition of $n$, let $h_{ij}(\lambda)$ denote the hook length of cell $(i,j)$ in the Young diagram of $\lambda$. Is there a closed formula or a generating function for the ...
0answers
36 views

### Higher order Leibniz rule and ordered multiindex notation

Although I think this is probably known, I am making here a short exposition on the multiindex notations I am using to make this question self-contained. I note that there is at least two different ...
1answer
109 views

### Directed version of this lemma

On a paper by Shoham Letzter, available Here, there's a lemma that says as follows: Lemma 0: For every graph $G$, there exist two disjoint sets $U,W\subseteq V(G)$ of equal size, such that there are ...
1answer
60 views

### Number of linear inequalities describing a polyhedron with prescribed number of vertices

If a polytope has $d$ vertices in $k$ dimensions how many linear inequalities is required to describe it?
1answer
415 views

### Packing equal-size disks in a unit disk

Inspired by the delicious buns and Siu Mai in bamboo steamers I saw tonight in a food show about Cantonese Dim Sum, here is a natural question. It probably has been well studied in the literature, but ...
0answers
239 views

1answer
63 views

### Min-sum and min-max node-disjoint path problems

Given an undirected weighted graph, we seek a pair of node-disjoint path between $2$ nodes $s$ and $t$: if the objective is to minimize the total path cost, the Suurballe algorithm can be applied; now ...
2answers
235 views

### sum of odious numbers to the power of k

In number theory, an odious number is a positive integer that has an odd number of $1$s in its binary expansion. The first odious numbers are: \$1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, ...