8 papers
Flag vectors
Jonathan Fine
This paper defines for each object that can be constructed out of a finite number of vertices and cells a vector lying in a finite dimensional vector space. This is the fl…
Graphs, flags and partitions
Jonathan Fine
This paper defines, for each graph , a flag vector . The flag vectors of the graphs on vertices span a space whose dimension is , the number of partitions on .…
Stratified simplices and intersection homology
Jonathan Fine
Intersection homology is obtained from ordinary homology by imposing conditions on how the embedded simplices meet the strata of a space . In this way, for the middle perversity…
Ring structure, uniform expressions and intersection homology
Jonathan Fine
Although intersection homology lacks a ring structure, certain expressions (called uniform) in the intersection homology of an irreducible projective variety always give the sa…
Vassiliev theory and regional change
Jonathan Fine
The purpose of this note is to state some definitions that may be useful in the study of knots, manifolds and the like. They apply to anything for which the concept of a regional c…
Hodge's harmonic -sets and Pontrjagin classes
Jonathan Fine
This paper shows how Hodge's theory of harmonic -sets (a discrete version of his theory of harmonic forms) allows a new approach to be taken to the problem of providing a combin…