Search Results for ""

A partition p is said to contain another partition q if the Ferrers diagram of p contains the Ferrers diagram of q. For example, {3,3,2} (left figure) contains both {3,3,1} ...

The length of the largest-sized square contained within the Ferrers diagram of a partition. Its size can be determined using DurfeeSquare[f] in the Wolfram Language package ...

A formula for the number of Young tableaux associated with a given Ferrers diagram. In each box, write the sum of one plus the number of boxes horizontally to the right and ...

A relation between permutations p and q that exists if there is a sequence of transpositions such that each transposition increases the number of inversions (Stanton and ...

The number of elements greater than i to the left of i in a permutation gives the ith element of the inversion vector (Skiena 1990, p. 27).

A set-like object in which order is ignored, but multiplicity is explicitly significant. Therefore, multisets {1,2,3} and {2,1,3} are equivalent, but {1,1,2,3} and {1,2,3} ...

A data structure designed to allow repeated extraction of the smallest remaining key (Skiena 1990, p. 38).

A pyritohedron is an irregular dodecahedron composed of identical irregular pentagons. The name "pyritohedron" derives from that fact that a common crystal form in pyrite has ...

A random composition of a number n in k parts is one of the (n+k-1; n) possible compositions of n, where (n; k) is a binomial coefficient. A random composition can be given ...

A random partition of a number n is one of the P(n) possible partitions of n, where P(n) is the partition function P. A random partition can be given by RandomPartition[n] in ...