Combinatorics and geometry of power ideals

Transactions of the American Mathematical Society

Volumn 362, Issue 8, 2010, Pages 4357-4384

  Ardila, Federico ^a   Postnikov, Alexander ^b  

^a SAN FRANCISCO STATE UNIVERSITY   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77951646872     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-10-05018-X     Document Type: Article

References (25)

1. F. Ardila. Computing the Tutte polynomial of a hyperplane arrangement. Pacific J. Math. 230 (2007) 1-26. MR2318445 (2008g:52034)
2. F. Ardila. Enumerative and algebraic aspects of matroids and hyperplane arrangements. Ph.D. thesis, Massachusetts Institute of Technology, 2003.
3. V. Batyrev and O. Popov. The Cox ring of a del Pezzo surface. (English summary) Arithmetic of higher-dimensional algebraic varieties (Palo Alto, CA, 2002), 85-103. Progr. Math., 226, Birkhäuser Boston, Boston, MA, 2004. MR2029863 (2005h:14091)
4. A. Berget. Products of linear forms and Tutte polynomials. Preprint, 2008.
5. M. Brion and M. Arrangement of hyperplanes. I. Rational functions and Jeffrey-Kirwan residue. Ann. Sci. Ecole Norm. Sup. (4) 32 (1999) 715-741. MR1710758 (2001e:32039)
6. W. Dahmen and C. Micchelli. On the local linear independence of translates of a box spline. Studia Math. 82(3) (1985) 243-263. MR825481 (87k:41008)
7. C. De Concini and C. Procesi. Wonderful models of subspace arrangements. Selecta Math. (N.S.) 1 (1995) 459-494. MR1366622 (97k:14013)
8. C. De Concini and C. Procesi. The algebra of the box spline. Preprint, 2006. arXiv:math/0602019v1.
9. J. Emsalem and A. Iarrobino. Inverse system of a symbolic power. Journal of Algebra 174 (1995) 1080-1090. MR1337186 (96i:13017)
10. A. Geramita and H. Schenck. Fat Points, Inverse Systems, and Piecewise Polynomial Functions. J. of Algebra 204 (1998) 116-128. MR1623949 (99d:13019) (Pubitemid 128346367)
11. O. Holtz and A. Ron. Zonotopal algebra. Preprint, 2007. arXiv:0708.2632.
12. 2. Queen's Papers in Pure and Applied Mathematics. Queen's Univ., Kingston, Ontario, vol.123, 2002. MR1898832 (2003f:13032)
13. P. Orlik and H. Terao. Commutative algebras for arrangements. Nagoya Math. J., 134 (1994) 65-73. MR1280653 (95j:52025)
14. J. Oxley. Matroid Theory. Oxford University Press, New York, 1992. MR1207587 (94d:05033)
15. A. Postnikov, B. Shapiro. Trees, parking functions, syzygies, and deformations of monomial ideals. Transactions of the American Mathematical Society 356 (2004) 3109-3142. MR2052943 (2005a:05066) (Pubitemid 38920387)
16. A. Postnikov, B. Shapiro, M. Shapiro. Algebras of curvature forms on homogeneous manifolds. In Differential Topology, Infinite-Dimensional Lie Algebras, and Applications: D. B. Fuchs 60th Anniversary Collection, AMS Translations, Series 2 194 (1999) 227-235. MR1729365 (2001a:53079)
17. N. Proudfoot and D. Speyer. A broken circuit ring. Beiträge Algebra Geom. 47 (2006) 161-166. MR2246531 (2007c:13029)
18. S. Roman and G.C. Rota. The umbral calculus. Adv. in Math. 27 (1978) 95-188. MR0485417 (58:5256)
19. H. Schenck. Linear systems on a special rational surface. Mathematical Research Letters 11 (2004) 697-714. MR2106236 (2005j:14053) (Pubitemid 40131648)
20. A. Sokal. The multivariate Tutte polynomial (alias Potts model) for graphs and matroids. In Surveys in Combinatorics, 2005, edited by Bridget S. Webb (Cambridge University Press, 2005), pp. 173-226. MR2187739 (2006k:05052)
21. R. Stanley. Hyperplane arrangements. In Geometric Combinatorics (E. Miller, V. Reiner, and B. Sturmfels, eds.), IAS/Park City Mathematics Series, vol.13, American Mathematical Society, Providence, RI, 2007, pp. 389-496. MR2383131
22. B. Sturmfels and Z. Xu. Sagbi bases of Cox-Nagata rings. Preprint, 2008. arXiv:0803.0892.
23. H. Terao. Algebras generated by reciprocals of linear forms. J. Algebra 250 (2002) 549-558. MR1899865 (2003c:16052) (Pubitemid 36208383)
24. D. Wagner. Algebras related to matroids represented in characteristic zero. European J. Combin. 20 (1999) 701-711. MR1721927 (2001j:13002)
25. N. White (ed.). Matroid Applications. Cambridge University Press, Cambridge, 1992. MR1165537 (92m:05004)