We study the effects of imposing linear relations within modules matrices on average sizes kernels. The that we consider can be described combinatorially in terms partial colourings grids. cells these grids correspond to positions and each defining relation involves all a given colour. prove such arising from ‘admissible’ has no effect kernels over finite quotients discrete valuation rings. Thi...

Let H and K be subgroups of a group G. The double cosets of H and K in G are the sets HgK, g E G. In this paper we describe a procedure, P, for determining the cardinality of the set H\G/K of double cosets of H and K in G given a finite presentation for G and finite sets of generators for H and K. It is well known that the problem of determining whether or not a group G defined by a finite pres...

The method of graphical vertex-condensation for enumerating perfect matchings of plane bipartite graph was found by Propp (Theoret. Comput. Sci. 303(2003), 267-301), and was generalized by Kuo (Theoret. Comput. Sci. 319 (2004), 29-57) and Yan and Zhang (J. Combin. Theory Ser. A, 110(2005), 113125). In this paper, by a purely combinatorial method some explicit identities on graphical vertex-cond...

Recently, an algorithm called Freqt was introduced which enumerates all frequent induced subtrees in an ordered data tree. We propose a new algorithm for mining unordered frequent induced subtrees. We show that the complexity of enumerating unordered trees is not higher than the complexity of enumerating ordered trees; a strategy for determining the frequency of unordered trees is introduced.

We consider the problem of enumerating triangulations of n points in the plane in general position. We introduce a tree of triangulations and present an algorithm for enumerating triangulations in O(log log n) time per triangulation. It improves the previous bound by almost linear factor.

In this paper, we propose an algorithm for enumerating all the perfect matchings included in a given bipartite graph G = (V,E). The algorithm is improved by the approach which we proposed at ISAAC98. Our algorithm takes O(log |V |) time per perfect matching while the current fastest algorithm takes O(|V |) time per perfect matching. Keyword: enumeration, enumerating algorithm, perfect matching.