Questions tagged [combinatorics]

Combinatorics is the branch of computer science and math that focuses on the enumerable arrangements of a finite set. This includes permutations, combinations, and partitions.

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Spreading objects in bags and bags' compartments

We have 10 bags. Each bag has 5 compartments numbered from 1 to 5. We have 100 objects to fill all the compartments and bags. Compartment number x in a bag is identical to compartment of the same ...
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Why does the last phase of Irving's Stable Roommates Matching work

Pertaining to the Stable Roommates Problem and the algorithm developed by Robert W. Irving. There are two (sometimes broken into three) phases in which we may come to a stable pairing of everyone in ...
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What algorithm to use to count realization of high combinatorics setup?

I'll use the MobA games to illustrate what I'm asking since it's easier to explain even tho I want to apply that algorithm to time series. In a MobA game you have more than 100 characters and every ...
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Domain analysis for discrete values - ON and OFF points in these cases

Following my previous question (with great answer from Bart van Ingen Schenau), I noticed a discrepancy I could not wrap my head around: Bart mentioned that: The point ON the boundary is by ...
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Why isn't this combinatorial solution equivalent to the recursive solution for finding the number of “paths”?

Here's the problem: Given an m x n array, get the number of different paths from the top left corner to the bottom right corner, if you can only move down, right, and diagonally down & right. ...
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How to calculate binomial coefficient C(n, r) modulo some prime power?

How to calculate C(n, r) modulo m, m is of the form p^a, where p is prime. Here C(n, r) means n choose r. The range of n and r is large (of the order of 10^18) so it cannot be solved by calculating ...