Linear extension sums as valuations on cones

Adrien Boussicault, Valentin Féray, Alain Lascoux, Victor Reiner

Research output: Contribution to journalArticlepeer-review

10 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

Bibliographical note

Funding Information:
Acknowledgements This work began during a sabbatical visit of V.R. to the Institut Gaspard Monge at the Université Paris-Est, and he thanks them for their hospitality. He is also grateful to Prof. Michelle Vergne for an enlightening explanation of total residues. This work was finished during a visit of the second author to the University of Minnesota, and he thanks them for the invitation and the welcoming environment. The authors also would like to thank an anonymous referee for helpful comments. Fourth author was supported by NSF grant DMS-0601010.

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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