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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2
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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 ...
2
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169
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Combinations of elements in array
I wrote this code to get all possible arrangements for an array containing 3 elements:
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Video Poker with luck modifier
While grinding for coins on the GTA San Andreas casino poker machines I started to
wonder how exactly one might implement a luck modifier to a video poker game without
it being completely obvious to ...
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Generating group permutations: an extended Heap's algorithm in Java
Suppose we have a sequence of sequences <1, 2> <3, 4>. There, we have two groups: <1, 2> and ...
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Schedule a series of 1:1 contests so that each entrant plays against every other
My sister is organizing a Majong tournament. She wants to set up a set of round-robin rounds.
There will be 16 players at 4 tables; 4 players per table. Players will play 5 rounds. She wants every ...
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Find the list of combination (with repetition) given rank and number of items. (Lexicographic ordering)
The problem involves the fastest possible method to generate a list of combinations which repeats from all the possible combinations with repetition allowed. I know there needs to be a way to ...
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String Permutation Implemention
The objective is simple: List all possible permutations for a given a String. I looked at some implementations from popular sources. I decided to build this to the flow:
The Code for Review
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Creates all possible permutations of a string and its substrings
I want to improve this code to efficiently create all possible permutations/combinations of a string. For example, if I have the string "abc", the result would be the list [ab, ac, ba, bc, ...
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Effective encoding-decoding chain determination (time optimization)
Could you please help with speeding-up this code?
Input: UTF-8 text (encoded 1-3 times from known pool of encodings). Every time was encoded and decoded by random encoding from pool. Original was koi8-...
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Find all combinations of length 3 whose sum is divisible by a given number
I came up with a suitable solution to a HackerRank problem that failed because the execution took longer than 10 seconds on lists that were of very large size.
The problem: Given a list ...
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Print all "balanced" sequences of 'A' and 'B'
the aim of the code below is to print all balanced sequences with equal number of 'A' and 'B'. A sequence is balanced if every prefix of length \$\geqslant 4\$ is balanced. A prefix is balanced if the ...
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Check if two semistandard Young tableaux are compatible
I have a question about how to check if two tableaux are compatible (will define below). Here we only consider tableaux of rectangular shape.
A tableau is called semistandard if its rows are weakly ...
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Iterating over all simple unique cycles in an undirected graph in Java - brute-force approach
This post is about an Iterator iterating over simple loops of an undirected graph.
In the above graph, the cycle \$\langle 1, 2, 3, 4, 5, 3, 1 \rangle\$ is not ...
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Query for sequential column permutations in SQLite
For dummy's sake, let's say that I have a database with columns text, ind and sentid. You ...
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An algorithm that minimizes the number of ingredients necessary
I am working on a code that will minimize the number of ingredients necessary to make some dishes.
Each dish can be prepared in an arbitrary large number of ways, with combinations of two ingredients. ...
- 485
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Boolean evaluation
Given a boolean expression consisting of the symbols 0 (false), 1 (true), & (AND), | (OR), and ^ (XOR), and a desired boolean result value result, implement a function to count the number of ways ...
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A more elegant way to uniformly sample from non-negative integers with a fixed sum
Given a positive integer n, I would like to randomly output n non negative integers that sum to ...
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Printing subarrays ⚡
I was trying to to print all subarrays of an array in quadratic time. Here is my code:
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Subarrays with length
You are given an array A of length N (where N is as large as 2×105). All elements of the array are positive integers less than or equal to N. Determine the count of subarrays (contiguous subsequences) ...
3
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Pascal's triangle solution in Python code
I have solved the pascal's triangle problem. I am not good at writing efficient programs, hence any suggestions/ comments shall be welcomed.
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Subset Product Algorithm
Subset Product is an NP-complete problem and is my favorite problem. So, I've written a slightly smarter way of solving the problem.
Will performance impact matter if I use multi-cpus and my GPU?
Do ...
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Find non-overlapping pairs of elements in a list whose difference is less than some given threshold
I have the following task: Let us have a list (denoted by L, and for simplicity, the elements come from the interval [0,1]). We are given a parameter (denoted by C), and we want to find as many pairs ...
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Count five-digit octal numbers with alternating even and odd digits, without repeated digits
I need to find the number of five-digit octal numbers in which all digits are different and no two odd or even digits are adjacent.
My code below gives the correct answer, but I'm not satisfied. Can ...
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Given a number of points, generates all paths between all points that does not overlap
I wrote this code in 4 days, I want to see if I can optimize this code some more, and have some suggestion on what can I improve.
This code takes in any number of points then naming them ...
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Minimum re-labeling to make an array as close as possible to another one
I have an array with integer labels in [0, n-1], say arr1=[1, 0, 3, 2] with n = 3. And then I have another array again with integer labels in [0, n-1], say arr2=[0, 0, 2, 3]. How can I find the ...
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Calculating all combinations from arrays AND (arrays OR floats)
Context: My question comes from needing to iterate different np.arange arrays. The main motivation is to calculate all the possible combinations between the arrays, ...
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Absolute Permutation | Hacker Rank: Any way to make this python code faster without changing it's whole logic?
https://www.hackerrank.com/challenges/absolute-permutation/problem
I know that if you work out the math and logic first, the algorithm can be simplified greatly (shifting indices), but is that the ...
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Finding possible combinations for n<7 with rust
I am trying to learn rust and as such have been redoing some of the challenges on project Rosalind. This one relates to the challenge Enumerating Gene Orders.
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Generate possible combinations by range and length
I am learning Haskell and I implemented a recursive function that generates possible strings by length and array (e.g. ['a'..'z']):
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Increase speed of lapply function identifying the sum of all existing combinations
I have a dataframe of cases that score 0-1 on a group of binary attributes.
What I want to do is extract all possible ombinations of attribute triplets (e.g. A/B/C, A/B/D... out of A-E) and then sum ...
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In how many different ways can a group of 9 people be divided into 3 groups, with each group containing 3 people?
To divide 9 persons into 3 groups, when the ordering of groups is not important can be done in
(9C3 * 6C3 * 3C3) / (3!) = 280 ways
Here, we divide by (3!) because the ordering of 3 groups is not ...
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Loop through the nearest switch and deletion neighbours of a Boolean assignment
My goal is to look for nearest neighbours in a Boolean-assigned mapping (a Python dictionary). For this purpose I'm looping through the candidates, starting from those with the closest distance. The ...
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Generate all subsets of a set
The goal of the function below is to generate all subsets of a given set, i.e. a collection of sets that contain all possible combinations of the elements in the set. Note that for my application I do ...
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Building a tree containing all permutations of arithmetic expressions given some numbers
Given any series of numbers, for example 1,2,3,4,5 and given the arithmetic operands + - * / including parenthesis, what would be the most optimal way to build a tree that contains all permutations ...
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Find all combinations of numbers of a set that add up to a given target - avoid for loops
I am thinking about the following problem:
Consider a 3-numbers lock, i.e. a lock which has three little number wheels that opens whenever the sum of these three numbers equals 75. I know, this doesn'...
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