In this work we study permutation synchronisation for the challenging case of partial permutations, which plays an important role for the problem of matching multiple objects (e.g. images or shapes). The term synchronisation refers to the property that the set of pairwise matchings is cycle-consistent, i.e. in the full matching case all compositions of pairwise matchings over cycles must be equ...

In this paper we rst show that the permutation-path coloring problem is NP-hard even for very restrictive instances like involutions, which are permutations that contain only cycles of length at most two, on both binary trees and on trees having only two vertices with degree greater than two, and for circular permutations which are permutations that contain exactly one cycle on trees with maxim...

We prove some general results about the asymptotics of the distribution of the number of cycles of given length of a random permutation whose distribution is invariant under conjugation. These results were first established to be applied in a forthcoming paper [BG], where we prove results about cycles of random permutations which can be written as free words in several independent random permut...

Authenticated encryption schemes establish both privacy and authenticity. This paper specifies a family of the dedicated authenticated encryption schemes, Artemia. It is an online nonce-based authenticated encryption scheme which supports the associated data. Artemia uses the permutation based mode, JHAE, that is provably secure in the ideal permutation model. The scheme does not require the in...

The toughness of a graph G is the minimum of |S|/k(G − S) over all sets S of vertices such that k(G − S) ≥ 2. In this paper upper bounds on the toughness of a cubic graph are derived in terms of the independence number and coloring parameters. These are applied to cycle permutation graphs. Running head: as per title.

We study the mixing properties of permutations obtained as a product of two uniformly random permutations of fixed cycle types. For instance, we give an exact formula for the probability that elements 1, 2, . . . , k are in distinct cycles of the random permutation of {1, 2, . . . , n} obtained as product of two uniformly random n-cycles.

An algorithm is constructed for recognizing the circulant graphs and finding a canonical labeling for them in polynomial time. This algorithm also yields a cycle base of an arbitrary solvable permutation group. The consistency of the algorithm is based on a new result on the structure of Schur rings over a finite cyclic group. §

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fai...

First cycle games (FCG) are played on a finite graph by two players who push a token along the edges until a vertex is repeated, and a simple cycle is formed. The winner is determined by some fixed property Y of the sequence of labels of the edges (or nodes) forming this cycle. These games are traditionally of interest because of their connection with infinite-duration games such as parity and ...