Results 1  10
of
871
Combinatorial invariants of algebraic Hamiltonian actions
"... Abstract. To any Hamiltonian action of a reductive algebraic group G on a smooth irreducible symplectic variety X we associate certain combinatorial invariants: Cartan space, Weyl group, weight and root lattices. Actually, only the last definition is new. For cotangent bundles our invariants essenti ..."
Abstract

Cited by 5 (5 self)
 Add to MetaCart
Abstract. To any Hamiltonian action of a reductive algebraic group G on a smooth irreducible symplectic variety X we associate certain combinatorial invariants: Cartan space, Weyl group, weight and root lattices. Actually, only the last definition is new. For cotangent bundles our invariants
Combinatorial invariance of StanleyReisner rings
 315–318. PROBLEMS OF TORIC MANIFOLDS 15
, 1996
"... Abstract. In this short note we show that Stanley–Reisner rings of simplicial complexes, which have had a “dramatic application ” in combinatorics [2, p. 41], possess a rigidity property in the sense that they determine their underlying simplicial complexes. For convenience we recall the notion of a ..."
Abstract

Cited by 11 (1 self)
 Add to MetaCart
Abstract. In this short note we show that Stanley–Reisner rings of simplicial complexes, which have had a “dramatic application ” in combinatorics [2, p. 41], possess a rigidity property in the sense that they determine their underlying simplicial complexes. For convenience we recall the notion of a Stanley–Reisner ring (for more information the reader is referred to [1, Ch. 5]). Let V be a finite set to be simplicial complex (on the vertex set V) if the following conditions hold: (a) {v} ∈ ∆ for any element v ∈ V, (b) σ ′ ∈ ∆ whenever σ ′ ⊂ σ for some σ ∈ ∆. Elements of ∆ will be called faces. Now assume we are given a field k and an abstract simplicial complex ∆ on a vertex set V. The Stanley–Reisner ring corresponding to these data is defined as the quotient ring of the polynomial ring k[v1,..., vn]/I, where n = #(V), the vi are the elements of V, and the ideal I is generated by the set of monomials {vi1 · · · vik {vi1,..., vik} / ∈ ∆}. This kalgebra will be denoted by k[∆] and called the Stanley–Reisner ring of ∆. Further, the image of vi in it will again be denoted by vi (they are all different!) and hence will again be thought of as elements of V. Theorem. Let k be a field, and ∆ and ∆ ′ be two abstract simplicial complexes defined on the vertex sets V = {v1,..., vn} and U = {u1,..., um} respectively. Suppose k[∆] and k[ ∆ ′ ] are isomorphic as kalgebras. Then there exists a bijective mapping Ψ: V → U which induces an isomorphism between ∆ and ∆ ′. Proof. Let f: k[∆] → k[ ∆ ′ ] be a kisomorphism. By scalar extension we may assume k is algebraically closed. Let us first show that without loss of
Combinatorial invariants for graph isomorphism problem.
, 804
"... Presented approach in polynomial time calculates large number of invariants for each vertex, which won’t change with graph isomorphism and should fully determine the graph. For example numbers of closed paths of length k for given starting vertex, what can be though as the diagonal terms of kth pow ..."
Abstract
 Add to MetaCart
Presented approach in polynomial time calculates large number of invariants for each vertex, which won’t change with graph isomorphism and should fully determine the graph. For example numbers of closed paths of length k for given starting vertex, what can be though as the diagonal terms of k
Combinatorial Invariants from Four Dimensional Lattice Models
, 1993
"... We study the subdivision properties of certain lattice gauge theories based on the groups Z2 and Z3, in four dimensions. The Boltzmann weights are shown to be invariant under all type (k,l) subdivision moves, at certain discrete values of the coupling parameter. The partition function then provides ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
a combinatorial invariant of the underlying simplicial complex, at least when there is no boundary. We also show how an extra phase factor arises when comparing Boltzmann weights under the Alexander moves, where the boundary undergoes subdivision. ITFA9306 / YCTPP693
The rational homology of toric varieties is not a combinatorial invariant
 PROC. AMER. MATH. SOC
, 1989
"... We prove that the rational homology Betti numbers of a toric variety with singularities are not necessarily determined by the combinatorial type of the fan which defines it; that is, the homology is not determined by the partially ordered set formed by the cones in the fan. We apply this result to t ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
We prove that the rational homology Betti numbers of a toric variety with singularities are not necessarily determined by the combinatorial type of the fan which defines it; that is, the homology is not determined by the partially ordered set formed by the cones in the fan. We apply this result
Combinatorial invariants computing the RaySinger analytic torsion
, 1996
"... Let K denote a closed odddimensional smooth manifold and let E be a flat vector bundle over K. In this situation the construction of Ray and Singer [RS] gives a metric on the determinant line of the cohomology det H ∗ (M; E) which is a smooth invariant of the manifold M and the flat bundle E. (Note ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
Let K denote a closed odddimensional smooth manifold and let E be a flat vector bundle over K. In this situation the construction of Ray and Singer [RS] gives a metric on the determinant line of the cohomology det H ∗ (M; E) which is a smooth invariant of the manifold M and the flat bundle E
KazhdanLusztig polynomials: History Problems, and Combinatorial Invariance
, 2003
"... Europe", grant HPRNCT200100272. We write elements of S n in three ways, namely: . disjoint cycle form (e.g., # = (7, 5, 2)(1, 3)) ; . oneline notation (e.g., # = 3714265); (Meaning that #(1) = 3, #(2) = 7, etc...) . matrix (e.g. # = 6 6 6 6 6 6 6 6 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
combinatorial objects related to KazhdanLusztig and Rpolynomials. The Bruhat graph of S n is the directed graph B(S n )
A combinatorial invariant for Spherical CR structures
"... We study a crossratio of four generic points of S 3 which comes from spherical CR geometry. We construct a homomorphism from a certain group generated by generic configurations of four points in S 3 to the preBloch group P(C). If M is a 3dimensional spherical CR manifold with a CR triangulation, ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
, by our homomorphism, we get a P(C)valued invariant for M. We show that when applying to it the BlochWigner function, it is zero. Under some conditions on M, we show the invariant lies in the Bloch group B(k), where k is the field generated by the crossratio. For a CR triangulation of Whitehead link
Results 1  10
of
871