Counting Shi Regions with a Fixed Separating Wall. Fishel, S., Tzanaki, E., & Vazirani, M. Ann. Comb., 17(4):671–693, 2013.
Counting Shi Regions with a Fixed Separating Wall [link]Paper  doi  bibtex   
@article {FTV2013,
    AUTHOR = {Fishel, Susanna and Tzanaki, Eleni and Vazirani, Monica},
     TITLE = {Counting {S}hi {R}egions with a {F}ixed {S}eparating {W}all},
   JOURNAL = {Ann. Comb.},
  FJOURNAL = {Annals of Combinatorics},
    VOLUME = {17},
      YEAR = {2013},
    NUMBER = {4},
     PAGES = {671--693},
      ISSN = {0218-0006},
   MRCLASS = {20B30 (05A15)},
  MRNUMBER = {3129778},
       DOI = {10.1007/s00026-013-0201-x},
       URL = {http://dx.doi.org.ezproxy1.lib.asu.edu/10.1007/s00026-013-0201-x},
}
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