The p–p Rearrangement and Failure-Tolerance of Double p-ary Multirings and Generalized Hypercubes

It is shown that an arbitrary grouped p-element permutation can be implemented in a conflict-free way through the commutation of channels on the double p-ary multiring or the double p-ary hypercube. It is revealed that in arbitrary single-element permutations, these commutators display the property of the (p - 1)-nodal failure-tolerance and the generalized hypercube displays in addition the property of the (p - 1)-channel failure-tolerance.