Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4653464 | European Journal of Combinatorics | 2015 | 12 Pages |
Abstract
We study connections among structures in commutative algebra, combinatorics, and discrete geometry, introducing an array of numbers, called Borel’s triangle, that arises in counting objects in each area. By defining natural combinatorial bijections between the sets, we prove that Borel’s triangle counts the Betti numbers of certain Borel-fixed ideals, the number of binary trees on a fixed number of vertices with a fixed number of “marked” leaves or branching nodes, and the number of pointed pseudotriangulations of a certain class of planar point configurations.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Christopher A. Francisco, Jeffrey Mermin, Jay Schweig,