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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calculate Binomial coefficient over $2^n$ in Matlab

I want to calculate ${n \choose k}/2^n$ for moderate $n$ and $k$. In Matlab, use nchoosek(n,k) with $n=60$ and $k=30$ will give a warning: "Warning: Result may not ...
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gradient for ternary functions?

I've got a function of form $$f: (\mathbb{Z}_3)^n \rightarrow \mathbb{R}$$ to optimize, where $n$ is relatively large (the order of hundreds). Is it there a gradient-like notion for these type of ...
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144 views

Evolutionary algorithm - Traveling Salesman -fitness function

I'm trying to solve this problem using genetic algorithms and am having difficulty choosing the fitness function. My problem is a little different than the original Traveling Salesman Problem, since ...
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144 views

What strategies one can use to keep maximum number of non attacking pieces on an $n \times n$ chess board? [closed]

What are the strategies one can use to keep maximum number of non attacking pieces (all pieces other than pawn) on an $n\times n$ board? It is like an $n$-queen problem but here instead of only queen ...
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186 views

How can I compute whether a sequence is an even or odd permutation of an increasing sequence? [closed]

Variants of this question have been crossposted to Stack Overflow and Mathematics Stack Exchange. Additional answers may be found at these other sites. Computational Science People: I originally ...
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198 views

Trying to implement a simple/efficient combinations function in MATLAB

So, recently, I have found myself in the position of having to implement a combinations function in MATLAB. What I mean by this is the following: I simply need to list all possible combinations for an ...
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Parallel algorithm to use in place of PORTA?

We currently use PORTA software to find the list of facet-defining inequalities (FDI) for polytopes that we work with. For certain polytopes, PORTA works fine. But because it is a serial algorithm ...
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1answer
65 views

Improve optimization over 'mapping' of indices

I have two tables at my disposal, one work dataset and one reference dataset. Each dataset has got two columns, lets say these are fields A and B. I would like to associate the rows in the reference ...
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1answer
101 views

Generating lattice clusters/graphs in parallel

I'm trying to generate all graphs with n or fewer vertices that can be embedded in some lattice, eg square, triangular, Kagome. Do there exist algorithms to both enumerate and draw these graphs? What ...
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1answer
128 views

Algorithm for generating all cartesian products, without rotations

(Not sure if that's the right SX site? I don't need actual code, so…) I'm looking for an algorithm that generates all cartesian products for a list of sets, but skips tuples that are just rotations ...
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175 views

What is the probabilistic model behind sudoku grids?

I'm talking about the vanilla sudoku game, with 9x9 grids equally split into 9 regions. I've tried a few approaches to estimate the probability that a specific number is in a specific location, but I ...
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Enumerating hexahedral cell vertices and faces in arbitrary dimension

I have a Cartesian mesh in $d$ dimensions, and I would like to enumerate all the subcells of a given hexahedral cell. If I am just enumerating the vertices of a cell (or cells that contain a vertex) I ...