We prove that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. This implies that, in general, multiple DES-encry...
A sequence of reversals that takes a signed permutation to the identity is perfect if it preserves all common intervals between the permutation and the identity. The problem of com...
Keccak is one of the five hash functions selected for the final round of the SHA-3 competition and its inner primitive is a permutation called Keccakf. In this paper, we find t...
We introduce a statistic pmaj(P) for partitions of [n], and show that it is equidistributed with cr2, the number of 2-crossings, over all partitions of [n] with given sets of mini...
William Y. C. Chen, Ira M. Gessel, Catherine H. Ya...
Several optimization problems require finding a permutation of a given set of items that minimizes a certain cost function. These problems are naturally modelled in graph-theory t...
Livio Bertacco, Lorenzo Brunetta, Matteo Fischetti