We extend our earlier work on free reduction problems for 2-complexes K in 4-manifolds N (i.e., the problem of effecting, by a geometric deformation of K in N , the free reduction of the relator words in the presentation associated with K). Here, the problem is recast, with new results, in terms of 2-handle presentations of 4-manifolds. Let M∗ be the complement of the interior of a closed 3-bal...

A graph G is a minimal claw-free graph (m.c.f. graph) if it contains no K1,3 (claw) as an induced subgraph and if, for each edge e of G, G − e contains an induced claw. We investigate properties of m.c.f. graphs, establish sharp bounds on their orders and the degrees of their vertices, and characterize graphs which have m.c.f. line graphs. MSC 2000: 05C75, 05C07

for an $n$-gon with vertices at points $1,2,cdots,n$, the betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. in this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and betti numbers of the $s$-module $s/i$ where  $s=k[x_{1},cdots, x_{n}]$ and $i$ is the associated ideal to ...

We introduce a robust statistical approach to realization from Minimal Recursion Semantics representations. The approach treats realization as a translation problem, transforming the Dependency MRS graph representation to a surface string. Translation is based on a Synchronous Context-Free Grammar that is automatically extracted from a large corpus of parsed sentences. We have evaluated the new...

We present a constraint-based syntax-semantics interface for the construction of RMRS (Robust Minimal Recursion Semantics) representations from shallow grammars. The architecture is designed to allow modular interfaces to existing shallow grammars of various depth – ranging from chunk grammars to context-free stochastic grammars. We define modular semantics construction principles in a typed fe...