# Questions tagged [combinatorics]

The tag has no usage guidance.

36 questions
Filter by
Sorted by
Tagged with
97 views

### Reducing resource allocation problem to bipartite matching

There are a set of bins, $B$ and a set of resources $R$. Each $b \in B$ is associated with a set function $Z_b(S) : 2^R \rightarrow \mathbb{R}^+$. The resource allocation problem is to find a ...
112 views

### Results/concepts that also proved useful outside of their “home areas”

There are some results/concepts in TCS which are used in areas other than the "home area" where they emerged. For example, NP-completeness has complexity theory as its home area, but it is also used ...
165 views

272 views

### Counting distinct set covers

I'm given a universal set $N = \{1, 2, \dots, n\}$, a family of sets $\mathcal{F} = \{ S_1, S_2, \dots, S_m \}$, $S_i \subseteq N$, and I need to count the number of distinct ways to cover the ...
107 views

### On number of disjoint sets with small stack depth in a set of permutations

Given k-distinct permutations $\sigma_1,\sigma_2,...,\sigma_k \in S_n$ where $k \leq 2^{\sqrt{n}}$ and $k >1$ (note that k is much smaller than number of possible permutations on [n]), What is ...
104 views

### What's a good advanced textbook/resource for studying the complexity of counting and combinatorics?

I'm taking a class in enumerative combinatorics. The professor focusses on the complexity of solving combinatorics problems like partitions etc. I'm using Enumerative Combinatorics but it does not ...
104 views

### Partitions on Integer Permutations

Let $S_n$ be the set of all permutations of integers from $1$ to $n$. Let $P_1$ and $P_2$ be two partitions defined on $S_n$ as follows. $P_1$ is the set of all those permutations which have even ...
76 views

411 views

### Binary matrix column subset selection complexity

Given an $m \times n$ matrix ($m$ rows) containing only $0$'s and $1$'s, what is the complexity of finding an $m \times k$ submatrix (of $k$ columns) such that within the chosen submatrix there is no ...
212 views

### A non-trivial combinatorial optimization

So I stumble over this problem in which I couldn't find anything similar in the literature. I am not even sure if it is NP-hard or solvable in polynomial time. Any thought or suggestion would be ...
174 views

### Locally monotone Boolean function

I am unable to understand the definition of locally monotone Boolean function which is defined in Gotsman and Linial, "Spectral Properties of Threshold Functions", 1994, p. 40: A function $f$ is ...