Miscellaneous functions

dimension_specht_module(mu::Partition{T}) where T <: IntegerUnion -> ZZRingElem

Return the dimension of the Specht module for mu.

Examples

julia> print([dimension_specht_module(p) for p in partitions(4)])
ZZRingElem[1, 3, 2, 3, 1]

gram_determinant_specht_module(mu::Partition{T}) where T <: IntegerUnion

Return the determinant of the Gram matrix for the Specht module for mu, in factorized collected form.

Examples

julia> print(gram_determinant_specht_module(partition([4, 3, 2, 1])))
Vector{ZZRingElem}[[3, 1152], [5, 768], [7, 384]]