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Root polytopes, triangulations, and the subdivision algebra. I. (English) Zbl 1233.05215

MSC:
05E15 Combinatorial aspects of groups and algebras (MSC2010)
16S99 Associative rings and algebras arising under various constructions
52B11 \(n\)-dimensional polytopes
52B22 Shellability for polytopes and polyhedra
51M25 Length, area and volume in real or complex geometry
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[1] Matthias Beck and Sinai Robins, Computing the continuous discretely, Undergraduate Texts in Mathematics, Springer, New York, 2007. Integer-point enumeration in polyhedra. · Zbl 1114.52013
[2] A. Cayley, On the partitions of a polygon, Proc. Lond. Math. Soc. 22 (1890), 237-262. · JFM 23.0541.01
[3] Sergey Fomin and Anatol N. Kirillov, Quadratic algebras, Dunkl elements, and Schubert calculus, Advances in geometry, Progr. Math., vol. 172, Birkhäuser Boston, Boston, MA, 1999, pp. 147 – 182. · Zbl 0940.05070
[4] W. Fong, Triangulations and Combinatorial Properties of Convex Polytopes, Ph.D. Thesis, 2000.
[5] Israel M. Gelfand, Mark I. Graev, and Alexander Postnikov, Combinatorics of hypergeometric functions associated with positive roots, The Arnold-Gelfand mathematical seminars, Birkhäuser Boston, Boston, MA, 1997, pp. 205 – 221. · Zbl 0876.33011 · doi:10.1007/978-1-4612-4122-5_10 · doi.org
[6] Edward L. Green, Noncommutative Gröbner bases, and projective resolutions, Computational methods for representations of groups and algebras (Essen, 1997) Progr. Math., vol. 173, Birkhäuser, Basel, 1999, pp. 29 – 60. · Zbl 0957.16033
[7] Takayuki Hibi, Gröbner basis techniques in algebraic combinatorics, Sém. Lothar. Combin. 59 (2007/10), Art. B59a, 22. · Zbl 1193.13030
[8] A. N. Kirillov, On some quadratic algebras, L. D. Faddeev’s Seminar on Mathematical Physics, Amer. Math. Soc. Transl. Ser. 2, vol. 201, Amer. Math. Soc., Providence, RI, 2000, pp. 91 – 113. · Zbl 0966.05080 · doi:10.1090/trans2/201/07 · doi.org
[9] A. N. Kirillov, personal communication, 2007.
[10] Alexander Postnikov, Permutohedra, associahedra, and beyond, Int. Math. Res. Not. IMRN 6 (2009), 1026 – 1106. · Zbl 1162.52007 · doi:10.1093/imrn/rnn153 · doi.org
[11] V. Reiner, Quotients of Coxeter complexes and P-Partitions, Ph.D. Thesis, 1990. · Zbl 0751.06002
[12] Victor Reiner, Signed posets, J. Combin. Theory Ser. A 62 (1993), no. 2, 324 – 360. · Zbl 0773.06008 · doi:10.1016/0097-3165(93)90052-A · doi.org
[13] R. Stanley, Catalan addendum (version of 20 September 2007), http://www-math.mit.edu/ \( \sim\)rstan/ec/catadd.pdf.
[14] Richard P. Stanley, Combinatorics and commutative algebra, 2nd ed., Progress in Mathematics, vol. 41, Birkhäuser Boston, Inc., Boston, MA, 1996. · Zbl 0838.13008
[15] Richard P. Stanley, Enumerative combinatorics. Vol. 2, Cambridge Studies in Advanced Mathematics, vol. 62, Cambridge University Press, Cambridge, 1999. With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin. · Zbl 0928.05001
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