Teaching:
Honors calculus 3, honors calculus 4, and 3283W (Sequences, series, and foundations).
Publications:
Differential posets and Smith normal forms
(with V. Reiner)
Abstract:
We conjecture a strong property for the up and down maps U and D in an
r-differential poset: DU+tI and UD+tI have Smith normal forms over Z[t]. In
particular, this would determine the integral structure of the maps U, D, UD,
DU, including their ranks in any characteristic.
As evidence, we prove the conjecture for the Young-Fibonacci lattice YF
studied by Okada and its r-differential generalizations Z(r), as well as
verifying many of its consequences for Young's lattice Y and the r-differential
Cartesian products Y^r.
(To appear in ORDER. Math ArXiv preprint arXiv:0811.1983)
Related invited talks:
Fields Institute Algebraic Combinatorics Seminar. Toronto, Canada. Jan., 2009.
University of Minnesota Combinatorics Seminar. Minneapolis, MN. March, 2008.
Note on 1-crossing partitions
(with M. Bergerson, V. Reiner, P. Shearer, D. Stanton, and N. Switala) To appear in Ars Combinatoria.
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