# Questions tagged [combinatorics]

For questions about the study of finite or countable discrete structures, especially how to count or enumerate elements in a set (perhaps of all possibilities) or any subset. It includes questions on permutations, combinations, bijective proofs, and generating functions.

8 questions
Filter by
Sorted by
Tagged with
1 vote
98 views

### How to solve assignment problem with additional constraints?

The assignment problem is defined as: Let there be n agents and m tasks. Any agent can be assigned to perform any task, incurring some costs that may vary depending on the agent-task assignment. We ...
189 views

### Use GA for Assignment Problem?

I have a two-objective assignment problem that appears to converge really slowly to a solution. Even if we just have 1 objective that minimizes costs, it appears to be very slow for a worker-task ...
96 views

### How many clues make Sudoku polynomial

Consider a $n^2 \times n^2$ grid sudoku. Define a clue to be composed of a coordinate $x$ and $y$ of the grid and a value $z$. The goal is given $n$ and a set of clues, to find one solution to the ...
1 vote
175 views

### Minimum vertex cover and linear programming 2

This is a modified version of the algorithm that I have proposed here. Suppose we have a graph G. Consider the minimum vertex cover problem of G formulated as a linear programming problem, that is for ...
One of the most commonly known combinatorial problems is the set cover problem, which states that given a collection of sets $S = \{s_1, \dots, s_m\}$ and a universe of elements $U = \bigcup_{i=1}^m ... 4 votes 1 answer 224 views ### Combinatorial Optimisation, Allocation problem I am trying to solve a problem (in pyspark/ python) where I need to find two distinct values to allocate, and how to allocate them in a network of stores. The two distinct values can only be integer ... 7 votes 1 answer 565 views ### Minimum vertex cover and linear programming Suppose we have a graph G. Consider the minimum vertex cover problem of G formulated as a linear programming problem, that is for each vertex$v_{i}$we have the variable$x_{i}$, for each edge$v_{i}...
In statistics, one often encounters the choose function ${x \choose y}$ which encodes the number of ways of choosing $y$ items from a set of $x$ items. How would one go about modeling a choose ...