Search results for "Mathematics::Combinatorics"
showing 10 items of 81 documents
Symmetric and finitely symmetric polynomials on the spaces ℓ∞ and L∞[0,+∞)
2018
We consider on the space l∞ polynomials that are invariant regarding permutations of the sequence variable or regarding finite permutations. Accordingly, they are trivial or factor through c0. The analogous study, with analogous results, is carried out on L∞[0,+∞), replacing the permutations of N by measurable bijections of [0,+∞) that preserve the Lebesgue measure.
Statistics-preserving bijections between classical and cyclic permutations
2012
Recently, Elizalde (2011) [2] has presented a bijection between the set C"n"+"1 of cyclic permutations on {1,2,...,n+1} and the set of permutations on {1,2,...,n} that preserves the descent set of the first n entries and the set of weak excedances. In this paper, we construct a bijection from C"n"+"1 to S"n that preserves the weak excedance set and that transfers quasi-fixed points into fixed points and left-to-right maxima into themselves. This induces a bijection from the set D"n of derangements to the set C"n"+"1^q of cycles without quasi-fixed points that preserves the weak excedance set. Moreover, we exhibit a kind of discrete continuity between C"n"+"1 and S"n that preserves at each s…
A segmentation algorithm for noisy images
2005
International audience; This paper presents a segmentation algorithm for gray-level images and addresses issues related to its performance on noisy images. It formulates an image segmentation problem as a partition of a weighted image neighborhood hypergraph. To overcome the computational difficulty of directly solving this problem, a multilevel hypergraph partitioning has been used. To evaluate the algorithm, we have studied how noise affects the performance of the algorithm. The alpha-stable noise is considered and its effects on the algorithm are studied. Key words : graph, hypergraph, neighborhood hypergraph, multilevel hypergraph partitioning, image segmentation and noise removal.
Gray code for derangements
2004
AbstractWe give a Gray code and constant average time generating algorithm for derangements, i.e., permutations with no fixed points. In our Gray code, each derangement is transformed into its successor either via one or two transpositions or a rotation of three elements. We generalize these results to permutations with number of fixed points bounded between two constants.
On mutually permutable products of finite groups
2005
Abstract In this paper a structural theorem about mutually permutable products of finite groups is obtained. This result is used to derive some results on mutually permutable products of groups whose chief factors are simple. Some earlier results on mutually permutable products of supersoluble groups appear as particular cases.
On totally permutable products of finite groups
2005
[EN] The behaviour of totally permutable products of finite groups with respect to certain classes of groups is studied in the paper. The results are applied to obtain information about totally permutable products of T, PT, and PST-groups.
Cyclic and lift closures for k…21-avoiding permutations
2011
We prove that the cyclic closure of the permutation class avoiding the pattern k(k-1)...21 is finitely based. The minimal length of a minimal permutation is 2k-1 and these basis permutations are enumerated by (2k-1).c"k where c"k is the kth Catalan number. We also define lift operations and give similar results. Finally, we consider the toric closure of a class and we propose some open problems.
A reconstruction algorithm for L-convex polyominoes
2006
AbstractWe give an algorithm that uniquely reconstruct an L-convex polyomino from the size of some special paths, called bordered L-paths.
When can an equational simple graph be generated by hyperedge replacement?
1998
Infinite hypergraphs with sources arise as the canonical solutions of certain systems of recursive equations written with operations on hypergraphs. There are basically two different sets of such operations known from the literature, HR and VR. VR is strictly more powerful than HR on simple hypergraphs. Necessary conditions are known ensuring that a VR-equational simple hypergraph is also HR-equational. We prove that two of them, namely having finite tree-width or not containing the infinite bipartite graph, are also sufficient. This shows that equational hypergraphs behave like context-free sets of finite hypergraphs.
Injectors and Radicals in Products of Totally Permutable Groups
2003
Abstract Two subgroups H and K of a group G are said to be totally permutable if every subgroup of H permutes with every subgroup of K. In this paper the behaviour of radicals and injectors associated to Fitting classes in a product of pairwise totally permutable finite groups is studied.