Genomic tableaux and combinatorial K-theory

Oliver Pechenik, Alexander Yong

Research output: Contribution to journalConference article

Abstract

We introduce genomic tableaux, with applications to Schubert calculus. We report a combinatorial rule for structure coefficients in the torus-equivariant K-theory of Grassmannians for the basis of Schubert structure sheaves. This rule is positive in the sense of [Anderson-Griffeth-Miller’11]. We thereby deduce an earlier conjecture of [Thomas-Yong’13] for the coefficients. Moreover, our rule specializes to give a new Schubert calculus rule in the (non-equivariant) K-theory of Grassmannians. From this perspective, we also obtain a new rule for K-theoretic Schubert structure constants of maximal orthogonal Grassmannians, and give conjectural bounds on such constants for Lagrangian Grassmannians.

Original languageEnglish (US)
Pages (from-to)37-48
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - Jan 1 2015
Event27th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2015 - Daejeon, Korea, Republic of
Duration: Jul 6 2015Jul 10 2015

Keywords

  • Equivariant K-theory
  • Genomic tableaux
  • Grassmannians
  • Schubert calculus

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)
  • Discrete Mathematics and Combinatorics

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