Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Combinatorics
Some of the functions here do not belong in combinatorics. I am including them here anyways.
Indexing
— Give the lexicographic index of a permutation
— Give the permutation corresponding to a given length and lexicographic index
— Give the index of a subset
— Get the subset with the given index and length
— Compute the index of a given tuple of non-negative integers
— Return the tuple corresponding to a given index
— Give the index of an ordered tuple
— Get the ordered tuple with the given index and length
— Create the Lehmer code corresponding to a given permutation
Partitions
— Switch the rows and columns of a partition
— Determine if one integer partition dominates another
— Check whether the argument is a weakly decreasing list of positive integers
— Get Dyson's crank of an integer partition
— Construct the corresponding partition, given a Frobenius symbol
— The largest part minus the number of parts of a partition
— Get a pair of lists representing the Ferrers diagram of a partition
— Display the Ferrers diagram of a partition with dots
— get the dimensions of the Durfee square of a partition
— test if a partition is a self-conjugate partition
Notation for partitions
— write a partition with plus signs, like 2+2+1
— go from a partition written with plus signs to a list of integers
Tableaux
— Determine if a list of values forms a Young tableau
— Transpose a Young tableau
— Get the two Young tableaux corresponding to a permutation
— Get a permutation corresponding to two Young tableaux
— Convert a Young tableau to a partially ordered set of coordinates
— Get a count of Young tableaux for a given size or shape
— Get the list of lists whose entries are the hook lengths of the entries of a Young tableau
— Enumerate all standard Young tableaux of a given shape
— Generate a random Young tableau with a given shape
Multisets
— canonical form of a multiset
— enumerate a multiset's partial derangements
— compute the multichoose operation
— assign every element of a multiset a unique number, in effect turning a multiset into a set.
— list the partial derangements of a multiset one by one
Make a list of the elements one by one
— Generate all possible orderless lists of a given length with a given set of elements
— Generate all possible orderless lists of a given length with a given set of unmarked indistinguishable plain unlabeled elements
Combinatorial Optimization and Existence
— Get permutations that satisfy a certain criterion
— Generate subsets that satisfy a certain criterion
— Generate tuples that satisfy a certain criterion
Combinatorial Functions
— compute the central binomial coefficient
— compute the Eulerian Catalan number
— Get the number of permutations with a given number of ascents
— compute the Eulerian number of the second kind
— compute the Narayana number
— compute the tangent numbers, also referred to as zag numbers
Encoding, Decoding, and Representation related
— Get the fibbinary sequence
— Fibonacci-digit encoding for a number
— Find the Gray code for an integer
— Find optimal Huffman code words given a list of probabilities
— Decode data specified by a Huffman encoding
— Find a Huffman encoding for a string
— Compute the inverse Fibonacci function
— Find the integer corresponding to a given Gray code
— Give the 0–1 list that indicates the unique nonconsecutive Fibonacci numbers that sum to the non-negative integer input
Permutation Functions
— Create the Lehmer code corresponding to a given permutation
— Get the next permutation in lexicographic order
— Give the indices of a permutation where there is an immediate ascent
— Compute the permutation graph of a permutation
— Give the lexicographic index of a permutation
— Give the permutation corresponding to a given length and lexicographic index
— Compute the major index of a permutation
— Get the two Young tableaux corresponding to a permutation
— Get a permutation corresponding to two Young tableaux
Permutation Inversion functions
— Construct the permutation list corresponding to the given inversion vector
— Count the number of pairs of out-of-order elements in a permutation
— Check if a list is the inversion vector of a permutation written as a list
— Get the number of permutations having a specified length and number of inversions
Permutation Runs and Ascents
— Split a list at its left-to-right maxima
— Give the indices of a permutation where there is an immediate ascent
MultisetStrictAscents
MultisetStrictAscentElements
— Give the indices of a permutation where there is an immediate descent
— Give the indices of a permutation of a multiset where there is an immediate descent
— Give a list of the elements that make up the descents of a multiset
— Get the number of permutations with a given number of ascents
— compute the Eulerian number of the second kind
Order Theory
— Generate a transitive reduction graph for the divisors of a positive integer
— Construct a Hasse diagram of a poset
— Test whether a graph is a partial order, that is, reflexive, antisymmetric and transitive
— Determine if a set of coordinates is partially ordered
— Convert a Young tableau to a partially ordered set of coordinates
— Test whether a graph is reflexive
— Test whether the binary relation defined by edges of a graph is transitive
Factorial Functions
— compute the Gauss factorial
— compute the phitorial
— compute the primorial
Recurrence Functions
— compute the term of the Lucas sequence of the first kind
— compute the term of the Lucas sequence of the second kind
Q Analogues
— q-exponential
— q-multinomial
Modular Number Theory
— find the period of a repeating decimal of a rational number
Alternating Permutations
— compute the tangent numbers, also referred to as zag numbers
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