Susanna Fishel ; Eleni Tzanaki ; Monica Vazirani - Counting Shi regions with a fixed separating wall

dmtcs:2916 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) - https://doi.org/10.46298/dmtcs.2916
Counting Shi regions with a fixed separating wallArticle

Authors: Susanna Fishel 1; Eleni Tzanaki 2; Monica Vazirani 3

  • 1 School of Mathematical and Statistical Sciences (Arizona, Tempe)
  • 2 Department of Applied Mathematics [Heraklion]
  • 3 Department of Mathematics [Univ California Davis]

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.

https://doi.org/10.46298/dmtcs.2916
Source: HAL:hal-01215106v1
Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Section: Proceedings
Published on: January 1, 2011
Imported on: January 31, 2017
Keywords: Shi arrangement,partitions,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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