Differential posets and Smith normal forms

Details Differential posets and Smith normal forms Differential posets and Smith normal forms

2008-11-12

arxiv.org/abs/0811.1983v1

Mathematics

Combinatorics

29 pages, 9 figures

Scientific paper

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.

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