Geodesic
Counting Shi regions with a fixed separating wall
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011).

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Athanasiadis introduced separating walls for a region in the extended Shi arrangement and used them to generalize the Narayana numbers. In this paper, we fix a hyperplane in the extended Shi arrangement for type A and calculate the number of dominant regions which have the fixed hyperplane as a separating wall; that is, regions where the hyperplane supports a facet of the region and separates the region from the origin. 
@article{DMTCS_2011_special_260_a29,
     author = {Fishel, Susanna and Tzanaki, Eleni and Vazirani, Monica},
     title = {Counting {Shi} regions with a fixed separating wall},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)},
     year = {2011},
     doi = {10.46298/dmtcs.2916},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2916/}
}
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Fishel, Susanna; Tzanaki, Eleni; Vazirani, Monica. Counting Shi regions with a fixed separating wall. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011). doi : 10.46298/dmtcs.2916. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2916/

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