Borel generators

Details Borel generators Borel generators

2010-06-08

arxiv.org/abs/1006.1436v2

Mathematics

Commutative Algebra

23 pages, 2 figures; very minor changes in v2. To appear in J. Algebra

Scientific paper

We use the notion of Borel generators to give alternative methods for computing standard invariants, such as associated primes, Hilbert series, and Betti numbers, of Borel ideals. Because there are generally few Borel generators relative to ordinary generators, this enables one to do manual computations much more easily. Moreover, this perspective allows us to find new connections to combinatorics involving Catalan numbers and their generalizations. We conclude with a surprising result relating the Betti numbers of certain principal Borel ideals to the number of pointed pseudo-triangulations of particular planar point sets.

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