2 research outputs found
ITERATIVE DECOMPOSITION OF PERMUTATIONS
Given symmetric group Sn and its subgroup (SqX Sp), P + q = n, we establish necessary
and sufficient conditions for the decomposition of Sn into left cosets of (SqX Sp) in Sn.
If n = 2m, (m = 1,2, ... ) and p = q = n/2 then by iteration we obtain a decomposition of
an arbitrary nE Sn in the form n = (f3~)(f3~, fig) ... (f3'/.r12-1, •.. , f3~\I), where N = logz nand
f3i is the j-th left coset leader obtained on the i-th stage. We develop an O(n log n) serial algorithm
for the programming the tree cellular permutations networks which result from the
above decomposition scheme