Cycles
From charlesreid1
What is a cycle
There are actually two definitions of cycles - one applies to problems involving permutations and combinatorics, while the other applies to graphs.
Combinatorics
In combinatorics, a cycle is a way to write a given permutation in a unique way using one-line notation.
(Permutations can also be written using two-line notation, where the first row consists of all items in their natural order, and the second row consists of the items in the order specified by the permutation, but the two-row representation is not unique.)
Graphs
On a graph, an Euler Cycle is a path through the graph that traverses every edge of the graph exactly once.
Related
Graphs:
Permutations:
Flags
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Combinatorics
Combinatorial Structures - Order Does Not Matter Ordinary generating functions
Labelled Structures - Order Matters Enumerating Permutations: String Permutations Generating Permutations: Cool · Algorithm M (add-one) · Algorithm G (Gray binary code)
Combinatorics Problems Longest Increasing Subsequence · Maximum Value Contiguous Subsequence · Racing Gems Cards (poker hands with a deck of 52 playing cards)
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The Art of Computer Programming notes from reading Donald Knuth's Art of Computer Programming
Volume 1: Fundamental Algorithms Mathematical Foundations: AOCP/Infinite Series · AOCP/Binomial Coefficients · AOCP/Multinomial Coefficients AOCP/Harmonic Numbers · AOCP/Fibonacci Numbers Puzzles/Exercises:
Volume 2: Seminumerical Algorithms AOCP/Random Numbers · AOCP/Positional Number Systems AOCP/Floating Point Arithmetic · AOCP/Euclids Algorithm AOCP/Factoring into Primes · AOCP/Polynomial Arithmetic AOCP/Power Series Manipulation
Volume 3: Sorting and Searching AOCP/Internal Sorting · AOCP/Optimal Sorting · AOCP/External Sorting AOCP/Binary Tree Searching · AOCP/Hashing AOCP/Combinatorics · AOCP/Multisets · Rubiks Cube/Permutations
AOCP/Combinatorial Algorithms · AOCP/Boolean Functions AOCP/Five Letter Words · Rubiks Cube/Tuples AOCP/Generating Permutations and Tuples
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