Subtree and substar intersection numbers

Subtree and Substar Intersection Numbers

Chang, Y.-W., M.S. Jacobson, CL. Monma and D.B. West, Subtree and substar intersection numbers. Discrete Applied Mathematics 44 (1993) 205-220. We introduce the star number [free number] of a graph, being the minimum t such that G is the intersection graph of unions of t substars [subtrees] of a host tree. We study bounds on these parameters, compare them with interval number, and characterize ...

Modeling Extractive Sentence Intersection via Subtree Entailment

Sentence intersection captures the semantic overlap of two texts, generalizing over paradigms such as textual entailment and semantic text similarity. Despite its modeling power, it has received little attention because it is difficult for non-experts to annotate. We analyze 200 pairs of similar sentences and identify several underlying properties of sentence intersection. We leverage these ins...

Word Sequences and Intersection Numbers

There are certain sequences of words in the generators of a twogenerator subgroup of SL(2,C) that frequently arise in the Teichmüller theory of hyperbolic three-manifolds and Kleinian groups. In this paper we establish the connection between two such families, the family of Farey words that have been used by Keen-Series to understand the boundaries of the Quasifuchsian space of surfaces of type...

Algebraic and Tropical Intersection Numbers

We prove that if X,X are closed subschemes of a torus T over a non-Archimedean field K, of complementary codimension and with finite intersection, then the stable tropical intersection along a (possibly positive-dimensional, possibly unbounded) connected componentC of Trop(X)∩Trop(X) lifts to algebraic intersection points, with multiplicities. This theorem requires potentially passing to a suit...

Virtual Intersection Numbers