Cycles
From charlesreid1
A cycle is an important concept to Permutations and Combinatorics.
A cycle is a way of writing a unique permutation in a unique way. (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.)
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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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