Geodesic
Genomic Tableaux and Combinatorial $K$-Theory
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015).

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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. 
@article{DMTCS_2015_special_285_a26,
     author = {Pechenik, Oliver and Yong, Alexander},
     title = {Genomic {Tableaux} and {Combinatorial} $K${-Theory}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)},
     year = {2015},
     doi = {10.46298/dmtcs.2482},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2482/}
}
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%V DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
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Pechenik, Oliver; Yong, Alexander. Genomic Tableaux and Combinatorial $K$-Theory. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015). doi : 10.46298/dmtcs.2482. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2482/

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