Voir la notice de l'article provenant de la source Cambridge University Press
Ardila, Federico; Fink, Alex; Rincón, Felipe. Valuations for Matroid Polytope Subdivisions. Canadian journal of mathematics, Tome 62 (2010) no. 6, pp. 1228-1245. doi: 10.4153/CJM-2010-064-9
@article{10_4153_CJM_2010_064_9,
author = {Ardila, Federico and Fink, Alex and Rinc\'on, Felipe},
title = {Valuations for {Matroid} {Polytope} {Subdivisions}},
journal = {Canadian journal of mathematics},
pages = {1228--1245},
year = {2010},
volume = {62},
number = {6},
doi = {10.4153/CJM-2010-064-9},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-064-9/}
}
TY - JOUR AU - Ardila, Federico AU - Fink, Alex AU - Rincón, Felipe TI - Valuations for Matroid Polytope Subdivisions JO - Canadian journal of mathematics PY - 2010 SP - 1228 EP - 1245 VL - 62 IS - 6 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-064-9/ DO - 10.4153/CJM-2010-064-9 ID - 10_4153_CJM_2010_064_9 ER -
%0 Journal Article %A Ardila, Federico %A Fink, Alex %A Rincón, Felipe %T Valuations for Matroid Polytope Subdivisions %J Canadian journal of mathematics %D 2010 %P 1228-1245 %V 62 %N 6 %U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-064-9/ %R 10.4153/CJM-2010-064-9 %F 10_4153_CJM_2010_064_9
[1] [1] Ardila, F., The Catalan matroid. J. Combin. Theory Ser. A 104(2003), no. 1, 49–62. doi:10.1016/S0097-3165(03)00121-3 Google Scholar
[2] [2] Björner, A., Las Vergnas, M., Sturmfels, B., White, N., and Ziegler, G. M., Oriented matroids. Encyclopedia of Mathematics and its Applications, 46, Cambridge University Press, Cambridge, 1993. Google Scholar
[3] [3] Billera, L. J., Jia, N., and Reiner, V., A quasisymmetric function for matroids. European J. Combin. 30(2009), no. 8, 1727–1757. doi:10.1016/j.ejc.2008.12.007 Google Scholar
[4] [4] Bonin, J. and de Mier, A., Lattice path matroids: structural properties. European J. Combin. 27(2006), no. 5, 701–738. doi:10.1016/j.ejc.2005.01.008 Google Scholar
[5] [5] Borovik, A., Gelfand, I., and N., White, Coxeter matroids. Progress in Mathematics, 216, Birkhäuser Boston, Boston, MA, 2003. Google Scholar
[6] [6] Brylawski, T. and Oxley, J., The Tutte polynomial and its applications. In: Matroid applications, Encyclopedia Math. Appl., 40, Cambridge University Press, Cambridge, 1992, pp. 123–225. Google Scholar
[7] [7] Crapo, H. H., Single-element extensions of matroids. J. Res. Nat. Bur. Standards Sect. B 69B(1965), 55–65. Google Scholar
[8] [8] Crapo and W, H.. Schmitt, A free subalgebra of the algebra of matroids. European J. Combin. 26(2005), no. 7, 1066–1085. doi:10.1016/j.ejc.2004.05.006 Google Scholar
[9] [9] Derksen, H., Symmetric and quasi-symmetric functions associated to polymatroids. J. Algebraic Combin. 30(2009), no. 1, 43–86. doi:10.1007/s10801-008-0151-2 Google Scholar
[10] [10] Derksen, H. and Fink, A., Valuative invariants for polymatroids. Adv. Math., in press. Google Scholar
[11] [11] Dress and W, A..Wenzel, Valuated matroids. Adv. Math. 93(1992), no. 2, 214–250. doi:10.1016/0001-8708(92)90028-J Google Scholar
[12] [12] Gelfand, I., Goresky, R., Mac Pherson, R., and V. Serganova. Combinatorial geometries, convex polyhedra, and Schubert cells. Adv. in Math. 63(1987), no. 3, 301–316. doi:10.1016/0001-8708(87)90059-4 Google Scholar
[13] [13] Hacking, P., Keel, S., and J. Tevelev. Compactification of the moduli space of hyperplane arrangements. J. Algebraic Geom. 15(2006), no. 4, 657–680. Google Scholar
[14] [14] Kapranov, M. M., Chow quotients of Grassmannians I. In: I. M. Gel’fand Seminar, Adv. Soviet Math. 16, American Mathematical Society, Providence, RI, 1993, pp. 29–110. Google Scholar
[15] [15] Klivans, C., Combinatorial properties of shifted complexes. Ph.D. Thesis, Massachusetts Institute of Technology, 2003. Google Scholar
[16] [16] Lafforgue, L., Chirurgie des grassmanniennes. CR M Monograph Series, 19, American Mathematical Society, Providence, RI, 2003. Google Scholar
[17] [17] Lafforgue, L., Pavages des simplexes, schémas de graphes recollés et compactification des PGLn+1 r /PGLr . Invent. Math. 136(1999), no. 1, 233–271. doi:10.1007/s002220050309 Google Scholar
[18] [18] Mc Mullen, P., Valuations and dissections. In: Handbook of convex geometry. North-Holland Publishing Co., Amsterdam, 1993, pp. 933–988. Google Scholar
[19] [19] Oxley, J. G., Matroid theory. Oxford University Press, New York, 1992. Google Scholar
[20] [20] Rota, G.-C., On the foundations of combinatorial theory. I. Theory of Möbius functions. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 2(1964), 340–368. doi:10.1007/BF00531932 Google Scholar
[21] [21] Rudin, W., Functional analysis. Mc Graw-Hill Series in Higher Mathematics, Mc Graw-Hill, New York, 1973. Google Scholar
[22] [22] Schrijver, A., Combinatorial optimization. Polyhedra and efficiency. Algorithms and Combinatorics Series, 24, Springer-Verlag, Berlin, 2003, Chpts. 70–83. Google Scholar
[23] [23] Speyer, D., Tropical linear spaces. SIA M J. Discrete Math. 22(2008), no. 4, 1527–1558. doi:10.1137/080716219 Google Scholar
[24] [24] Speyer, D., A matroid invariant via the K-theory of the Grassmannian. Adv. Math. 221(2009), no. 3, 882–913. doi:10.1016/j.aim.2009.01.010 Google Scholar
[25] [25] Stanley, R. P., Enumerative combinatorics, vol. 1. Cambridge Studies in Advanced Mathematics, 49, Cambridge University Press, Cambridge, 1997. Google Scholar
Cité par Sources :