Geodesic
Rational Shi tableaux and the skew length statistic
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020).

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We define two refinements of the skew length statistic on simultaneous core partitions. The first one relies on hook lengths and is used to prove a refined version of the theorem stating that the skew length is invariant under conjugation of the core. The second one is equivalent to a generalisation of Shi tableaux to the rational level of Catalan combinatorics. We prove that the rational Shi tableau is injective. Moreover we present a uniform definition of the rational Shi tableau for Weyl groups and conjecture injectivity in the general case. 
@article{DMTCS_2020_special_379_a31,
     author = {Sulzgruber, Robin},
     title = {Rational {Shi} tableaux and the skew length statistic},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)},
     year = {2020},
     doi = {10.46298/dmtcs.6349},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6349/}
}
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Sulzgruber, Robin. Rational Shi tableaux and the skew length statistic. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020). doi : 10.46298/dmtcs.6349. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6349/

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