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When the edges in a tree or rooted tree fail with a certain fixed probability, the (greedoid) rank may drop. We compute the expected rank as a polynomial in p and as a real number under the assumption of uniform distribution. We obtain several different expressions for this expected rank polynomial for both trees and rooted trees, one of which is especially… (More)

We define two two-variable polynomials for rooted trees and one two-variable polynomial for unrooted trees, all of which are based on the corank-nullity formulation of the Tutte polynomial of a graph or matroid. For the rooted polynomials, we show that the polynomial completely determines the rooted tree, i.e., rooted trees TI and T, are isomorphic if and… (More)

The greedoid Tutte polynomial of a tree is equivalent to a generating function that encodes information about the number of subtrees with I internal (non-leaf) edges and L leaf edges, for all I and L. We prove that this information does not uniquely determine the tree T by constructing an infinite family of pairs of non-isomorphic caterpillars, each pair… (More)

- Gary Gordon
- 1997

We extend Crapo's invariant from matroids to greedoids, concentrating especially on antimatroids. Several familiar expansions for (G) have greedoid analogs. We give combinatorial interpretations for (G) for simplicial shelling antimatroids associated with chordal graphs. When G is this antimatroid and b(G) is the number of blocks of the chordal graph G, we… (More)

Derangements are a popular topic in combinatorics classes. We study a generalization to face derangements of the n-dimensional hypercube. These derangements can be classified as odd or even, depending on whether the underlying isometry is direct or indirect, providing a link to abstract algebra. We emphasize the interplay between the geometry, algebra and… (More)

The notion of activities with respect to spanning trees in graphs was introduced by W.T. Tutte, and generalized to activities with respect to bases in matroids by H. Crapo. We present a further generalization, to activities with respect to arbitrary subsets of matroids. These generalized activities provide a unified view of several different expansions of… (More)

- Oleg K Glebov, Luz M Rodriguez, Kenneth Nakahara, Jean Jenkins, Janet Cliatt, Casey-Jo Humbyrd +12 others
- Cancer epidemiology, biomarkers & prevention : a…
- 2003

Distinct epidemiological and clinicopathological characteristics of colorectal carcinomas (CRCs) based on their anatomical location suggest different risk factors and pathways of transformation associated with proximal and distal colon carcinogenesis. These differences may reflect distinct biological characteristics of proximal and distal colonic mucosa,… (More)

We give an elementary procedure based on simple generating functions for constructing n (for any n >/2) pairwise non-isomorphic trees, all of which have the same degree sequence and the same number of paths of length k for all k >t 1. The construction can also be used to give a sufficient condition for isomorphism of caterpillars. In [2], a 2-variable… (More)

When G is a rooted graph where each edge may independently succeed with probability p, we consider the expected number of vertices in the operational component of G containing the root. This expected value EV (G; p) is a polynomial in p. We present several distinct equivalent formulations of EV (G; p), unifying prior treatments of this topic. We use results… (More)