skewGelfandTsetlinPatterns {syt}

Skew Gelfand-Tsetlin patterns

Description

Enumeration of Gelfand-Tsetlin patterns defined by a given skew partition and a given weight.

Usage

skewGelfandTsetlinPatterns(lambda, mu, weight)

Arguments

lambda, mu

integer partitions defining the skew partition: lambda is the outer partition and mu is the inner partition (so mu must be a subpartition of lambda); lambda will be the last row of the generated Gelfand-Tsetlin patterns and mu will be their first row

weight

integer vector; this vector will be the differences of the row sums of the generated Gelfand-Tsetlin patterns; consequently, there will be no generated Gelfand-Tsetlin pattern unless the sum of weight equals the difference between the sum of lambda and the sum of mu

Value

A list of matrices with non-negative integer entries. The number of columns of these matrices is the length of lambda and the number of rows of these matrices is one plus the length of weight.

See Also

GelfandTsetlinPatterns.

Examples

skewGelfandTsetlinPatterns(c(3, 1, 1), c(2), c(1, 1, 1))