Linear extension sums as valuations on cones

Adrien Boussicault, Valentin Féray, Alain Lascoux, Victor Reiner

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

The geometric and algebraic theory of valuations on cones is applied to understand identities involving summing certain rational functions over the set of linear extensions of a poset.

Original languageEnglish (US)
Pages (from-to)573-610
Number of pages38
JournalJournal of Algebraic Combinatorics
Volume35
Issue number4
DOIs
StatePublished - Jun 2012

Keywords

  • Affine semigroup ring
  • Hilbert series
  • Lattice points
  • Poset
  • Rational function identities
  • Root system
  • Total residue
  • Valuation of cones
  • Weight lattice

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    Boussicault, A., Féray, V., Lascoux, A., & Reiner, V. (2012). Linear extension sums as valuations on cones. Journal of Algebraic Combinatorics, 35(4), 573-610. https://doi.org/10.1007/s10801-011-0316-2