Differential posets and smith normal forms

Alexander Miller, Victor Reiner

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

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 Yr.

Original languageEnglish (US)
Pages (from-to)197-228
Number of pages32
JournalOrder
Volume26
Issue number3
DOIs
StatePublished - Sep 2009

Keywords

  • Differential poset
  • Dual graded graphs
  • Invariant factors
  • Smith normal form

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