Sym.Perm.Constructions

Sum, skew sum, etc

Documentation

(/+/) :: Perm -> Perm -> Perm infixl 6

The direct sum of two permutations.

(\-\) :: Perm -> Perm -> Perm infixl 6

The skew sum of two permutations.

directSum :: [Perm] -> Perm

The direct sum of a list of permutations.

skewSum :: [Perm] -> Perm

The skew sum of a list of permutations.

inflate :: Perm -> [Perm] -> Perm

inflate w vs is the inflation of w by vs. It is the permutation of length sum (map size vs) obtained by replacing each entry w!i by an interval that is order isomorphic to vs!i in such a way that the intervals are order isomorphic to w. In particular,

u /+/ v == inflate (mkPerm "12") [u,v]
u \-\ v == inflate (mkPerm "21") [u,v]