Questions tagged [combinatorics]
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.
501 questions
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Use z3py to solve one logic constraint puzzle
I decided to practice by modeling some simple, hand-solvable problems using z3py. Below is an example:
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Compute the flood polynomial of one graph using Mathematica
Reference: arXiv:2504.04233
Example 2.12: 4-vertex cycle graph
Structure: Square graph with 4 vertices
Flooding cascade sets: 7 total (2 of size 2, 4 of size 3, 1 of size 4)
Key insight: Opposite ...
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Demonstration of the Power Contamination Problem on Grids Revisited in Mathematica
The implementation successfully demonstrates all key findings from the research paper arXiv:2509.12756, including the disproof of the original conjecture and the establishment of the correct formula ...
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Expansion of the Rasala polynomials for symmetric group character degrees using Mathematica
I'd like to use Mathematica to demonstrate the expansion of the Rasala polynomials for symmetric group character degrees accroding to arXiv 2509.13190
The code is as follows. You may try it online!
<...
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Mathematica implementation of Lempel method for constructing Costas arrays
I ported C++ implementation of Lempel method for constructing Costas arrays to Mathematica.
How to fix my code? Thanks in advance.
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Mathematica implementation of Welch method for constructing Costas arrays
I ported C++ implementation of Welch method for constructing Costas arrays to Mathematica.
Any feedback would be appreciated.
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The Permutations Algorithm using BubbleSort and stack in PicoBlaze assembly language - attempt #2
So, this is improved code from my previous attempt to implement the permutations algorithm in PicoBlaze assembly language.
You can see it live here:
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Java program for calculating probabilities of die combinations in Yatzy
Yatzy
Yatzy is a dice rolling game where players aim to get particular die combinations.
This program counts probability of each such combinations. They are:
All five ones,
All five twos,
Same for ...
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Buy units of a good - If you buy them together, you get a discount - Find the cheapest way to purchase all goods available
The problem is as follows: A user needs to be able to purchase goods. He has a total of five distinct goods available: I've called them '1', '2', '3', '4', and '5',
If the user buys them in sets, he ...
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<Programming in Lua - 4th> exercise 2.2 - place 8 queens
About exercise 2.2
Place N queens on N*N board, 1 queen per line, so that all queens are safe.
Use permutation to improve the provided implementation from book.
The ...
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Finding the number of distinct decompositions a number has using only repdigits
This is a problem from a previous semester that I am trying to upsolve. I am trying to solve a problem involving the total number of ways of decomposing a number using only repdigits. A repdigit is a ...
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Find the join of two set partitions
Two partitions of a set have a greatest lower bound (meet) and a least upper bound (join).
See here: Meets and joins in the lattice of partitions (Math SE)
The meet is easy to calculate. I am trying ...
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Number of partitions of (a,b) into k distinct parts which sum up to (a,b)
Problem set
This is somewhat a generalization of the famous partition of integer n into k parts.
Given two integers ...
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Repetition-Limited Multiset Coefficient function
This is a simple multiset coefficient calculator in python, that will calculate both standard multiset coefficients, as well as multiset coefficients with repetition limits, used initially as part of ...
