InvolutionQ[p] yields True if permutation p is its own inverse.

Involutions[l] gives the list of involutions of the elements in the list l. Involutions[l, Cycles] gives the involutions in their cycle representation. Involution[n] gives ...

IsomorphicQ[g, h] yields True if graphs g and h are isomorphic.

Isomorphism[g, h] gives an isomorphism between graphs g and h if one exists. Isomorphism[g, h, All] gives all isomorphisms between graphs g and h. Isomorphism[g] gives the ...

IsomorphismQ[g, h, p] tests if permutation p defines an isomorphism between graphs g and h.

Josephus[n, m] generates the inverse of the permutation defined by executing every m\[Null]^th member in a circle of n members.

KnightsTourGraph[m, n] returns a graph with mn vertices in which each vertex represents a square in an m*n chessboard and each edge corresponds to a legal move by a knight ...

KSetPartitions[set, k] returns the list of set partitions of set with k blocks. KSetPartitions[n, k] returns the list of set partitions of {1, 2, ..., n} with k blocks. If ...

KSubsetGroupIndex[g, s, x] returns the cycle index of the k-subset group on s expressed as a polynomial in x[1], x[2], .... This function also takes the optional argument ...

KSubsetGroup[pg, s] returns the group induced by a permutation group pg on the set s of k-subsets of [n], where n is the index of pg. The optional argument Type can be ...