### 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 language | English (US) |
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Pages (from-to) | 37-48 |

Number of pages | 12 |

Journal | Discrete Mathematics and Theoretical Computer Science |

State | Published - Jan 1 2015 |

Event | 27th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2015 - Daejeon, Korea, Republic of Duration: Jul 6 2015 → Jul 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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## Cite this

*Discrete Mathematics and Theoretical Computer Science*, 37-48.