# Questions tagged [combinatorics]

Combinatorics (combinatorial analysis) is a branch of mathematics that studies the discrete objects, the set (a combination, permutation, deployment and transfer of elements) and the relationship to them (eg, partial order).

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### What is the generalization of the resource allocation problem I'm dealing with here?

I'm dealing with a problem as follows: I have a finite set of money 𝑚 to spend over 𝑟 different raffles, and I need to spend approximately to my budget, with the goal of maximizing my probability ...
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### Benchmark instances for directed 3-Cycle cover

The directed 3-Cycle cover asks for a vertex-covering set of oriented cycles with at least three vertices per cycle such that every vertex is covered by exactly one cycle. I have scrutinzed the ...
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### Determine minimum set to fulfil check criteria

Assume I have a list of companies which can be classified according to company type (LLC, LTD), number of employees (0, up to 5, more than 5) and field of operation (Banking, Leisure, Tourism). Every ...
36 views

### Integer partition algorithms

I am familiar with and have written MathCad algorithms for the partition functions 𝑝(𝑛,𝑘),which gives the number of ways of partitioning 𝑛 into 𝑘 parts, 𝑞(𝑛,𝑘), which gives the number of ways ...
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The quadratic knapsack problem (QKP) $$\max_x x^TPx$$ $$\mathrm{s.t.}\;\;w^Tx\leq c,\; x\in\{0,1\}$$ where $P\geq0, w\geq0$ elementwise, is well studied and has existing solvers. My problem below ...
45 views

### maximum eigenvalue across subsamples

I have an $N$-dimensional vector of data, say $X_{t}$, with $1 \leq t \leq T$. Of this vector $X_{t}$, I want to consider vectors, say $X_{t}^{b}$, which are $m$-dimensional combinations of elements ...
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### tea bag flavors mixing algorithm [closed]

I bought three boxes of tea bags with different flavors (A, B, C). I wish to mix them in such a way that - there is never two consecutive bags of the same flavor (ABCCAB is avoided) ; - the mixing ...