메뉴 건너뛰기




Volumn 75, Issue 255, 2006, Pages 1449-1466

Computing the Ehrhart quasi-polynomial of a rational simplex

Author keywords

Algorithm; Ehrhart quasi polynomial; Rational polytope; Valuation

Indexed keywords


EID: 33646721090     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-06-01836-9     Document Type: Article
Times cited : (36)

References (27)
  • 1
    • 0000303291 scopus 로고
    • New bounds in some transference theorems in the geometry of numbers
    • MR1233487 (94k:11075)
    • W. Banaszczyk, New bounds in some transference theorems in the geometry of numbers, Math. Ann. 296 (1993), 625-635. MR1233487 (94k:11075)
    • (1993) Math. Ann. , vol.296 , pp. 625-635
    • Banaszczyk, W.1
  • 3
    • 51249162823 scopus 로고
    • Computing the volume, counting integral points, and exponential sums
    • MR1220543 (94d:52005)
    • A. Barvinok, Computing the volume, counting integral points, and exponential sums, Discrete Comput. Geom. 10 (1993), 123-141. MR1220543 (94d:52005)
    • (1993) Discrete Comput. Geom. , vol.10 , pp. 123-141
    • Barvinok, A.1
  • 4
    • 0000975439 scopus 로고
    • A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed
    • MR1304623 (96c:52026)
    • A. Barvinok, A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed, Math. Oper. Res. 19 (1994), 769-779. MR1304623 (96c:52026)
    • (1994) Math. Oper. Res. , vol.19 , pp. 769-779
    • Barvinok, A.1
  • 5
    • 51249163698 scopus 로고
    • Computing the Ehrhart polynomial of a convex lattice polytope
    • MR1280575 (95e:52015)
    • A. Barvinok, Computing the Ehrhart polynomial of a convex lattice polytope, Discrete Comput. Geom. 12 (1994), 35-48. MR1280575 (95e:52015)
    • (1994) Discrete Comput. Geom. , vol.12 , pp. 35-48
    • Barvinok, A.1
  • 6
    • 0002646505 scopus 로고    scopus 로고
    • An algorithmic theory of lattice points in polyhedra
    • New perspectives in algebraic combinatorics (Berkeley, CA, 1996-97), Cambridge Univ. Press, Cambridge. MR1731815 (2000k:52014)
    • A. Barvinok and J. Pommersheim, An algorithmic theory of lattice points in polyhedra, New perspectives in algebraic combinatorics (Berkeley, CA, 1996-97), Math. Sci. Res. Inst. Publ., vol. 38, Cambridge Univ. Press, Cambridge, 1999, pp. 91-147. MR1731815 (2000k:52014)
    • (1999) Math. Sci. Res. Inst. Publ. , vol.38 , pp. 91-147
    • Barvinok, A.1    Pommersheim, J.2
  • 7
    • 0141680581 scopus 로고    scopus 로고
    • Short rational generating functions for lattice point problems
    • MR1992831 (2004e:05009)
    • A. Barvinok and K. Woods, Short rational generating functions for lattice point problems, J. Amer. Math. Soc. 16 (2003), 957-979. MR1992831 (2004e:05009)
    • (2003) J. Amer. Math. Soc. , vol.16 , pp. 957-979
    • Barvinok, A.1    Woods, K.2
  • 9
    • 0004125325 scopus 로고
    • A brief introduction to theta functions
    • Holt Rinehart and Winston, New York. MR0125252 (23:A2556)
    • R. Bellman, A Brief Introduction to Theta Functions, Athena Series: Selected Topics in Mathematics, Holt Rinehart and Winston, New York, 1961. MR0125252 (23:A2556)
    • (1961) Athena Series: Selected Topics in Mathematics
    • Bellman, R.1
  • 11
    • 4344582797 scopus 로고    scopus 로고
    • Effective lattice point counting in rational convex polytopes
    • MR2094541 (2005i:52020)
    • J. A. De Loera, R. Hemmecke, J. Tauzer, and R. Yoshida, Effective lattice point counting in rational convex polytopes, J. Symbolic Comput. 38(2004), 1273-1302; see also http://www.math.ucdavis.edu/~latte. MR2094541 (2005i:52020)
    • (2004) J. Symbolic Comput. , vol.38 , pp. 1273-1302
    • De Loera, J.A.1    Hemmecke, R.2    Tauzer, J.3    Yoshida, R.4
  • 14
    • 0031508084 scopus 로고    scopus 로고
    • The Ehrhart polynomial of a lattice polytope
    • Erratum: 146 (1997), no. 1, 237. MR1454701 (98e:11117a), MR1469320 (98e:11117b)
    • R. Diaz and S. Robins, The Ehrhart polynomial of a lattice polytope, Ann. of Math. (2) 145 (1997), 503-518; Erratum: 146 (1997), no. 1, 237. MR1454701 (98e:11117a), MR1469320 (98e:11117b)
    • (1997) Ann. of Math. (2) , vol.145 , pp. 503-518
    • Diaz, R.1    Robins, S.2
  • 15
    • 0011428975 scopus 로고
    • On the complexity of some basic problems in computational convexity. II. Volume and mixed volumes
    • Polytopes: Abstract, Convex and Computational (Scarborough, ON, 1993), Kluwer Acad. Publ., Dordrecht. MR1322071 (96k:52012)
    • P. Gritzmann and V. Klee, On the complexity of some basic problems in computational convexity. II. Volume and mixed volumes, Polytopes: Abstract, Convex and Computational (Scarborough, ON, 1993), NATO Adv. Sci. Inst. Ser. C. Math. Phys. Sci., vol. 440, Kluwer Acad. Publ., Dordrecht, 1994, pp. 373-466. MR1322071 (96k:52012)
    • (1994) NATO Adv. Sci. Inst. Ser. C. Math. Phys. Sci. , vol.440 , pp. 373-466
    • Gritzmann, P.1    Klee, V.2
  • 16
    • 0003957164 scopus 로고
    • Geometric algorithms and combinatorial optimization. Second edition
    • Springer-Verlag, Berlin. MR1261419 (95e:90001)
    • M. Grötschel, L. Lovász, and A. Schrijver, Geometric Algorithms and Combinatorial Optimization. Second edition, Algorithms and Combinatorics, vol. 2, Springer-Verlag, Berlin, 1993. MR1261419 (95e:90001)
    • (1993) Algorithms and Combinatorics , vol.2
    • Grötschel, M.1    Lovász, L.2    Schrijver, A.3
  • 17
    • 33645532485 scopus 로고    scopus 로고
    • Functional analysis
    • Wiley-Interscience, New York. MR1892228 (2003a:47001)
    • P. D. Lax, Functional Analysis, Pure and Applied Mathematics, Wiley-Interscience, New York, 2002. MR1892228 (2003a:47001)
    • (2002) Pure and Applied Mathematics
    • Lax, P.D.1
  • 18
    • 4244094761 scopus 로고    scopus 로고
    • Lectures on discrete geometry
    • Springer-Verlag, New York. MR1899299 (2003f:52011)
    • J. Matoušek, Lectures on Discrete Geometry, Graduate Texts in Mathematics, vol. 212, Springer-Verlag, New York, 2002. MR1899299 (2003f:52011)
    • (2002) Graduate Texts in Mathematics , vol.212
    • Matoušek, J.1
  • 19
    • 0001979028 scopus 로고
    • Lattice invariant valuations on rational polytopes
    • MR0526617 (80d:52011)
    • P. McMullen, Lattice invariant valuations on rational polytopes, Arch. Math. (Basel) 31 1978/79, 509-516. MR0526617 (80d:52011)
    • (1978) Arch. Math. (Basel) , vol.31 , pp. 509-516
    • McMullen, P.1
  • 20
    • 0001968639 scopus 로고
    • Valuations and dissections
    • North-Holland, Amsterdam. MR1243000 (95f:52018)
    • P. McMullen, Valuations and dissections, Handbook of Convex Geometry, vol. B, North-Holland, Amsterdam, 1993, pp. 933-988. MR1243000 (95f:52018)
    • (1993) Handbook of Convex Geometry , vol.B , pp. 933-988
    • McMullen, P.1
  • 21
    • 0002634852 scopus 로고
    • Valuations on convex bodies
    • Birkhäuser, Basel. MR0731112 (85e:52001)
    • P. McMullen and R. Schneider, Valuations on convex bodies, Convexity and its Applications, Birkhäuser, Basel, 1983, pp. 170-247. MR0731112 (85e:52001)
    • (1983) Convexity and Its Applications , pp. 170-247
    • McMullen, P.1    Schneider, R.2
  • 22
    • 0000058358 scopus 로고
    • Pick's theorem and the Todd class of a toric variety
    • MR1234309 (94j:14048)
    • R. Morelli, Pick's theorem and the Todd class of a toric variety, Adv. Math. 100 (1993), 183-231. MR1234309 (94j:14048)
    • (1993) Adv. Math. , vol.100 , pp. 183-231
    • Morelli, R.1
  • 23
    • 10044245751 scopus 로고    scopus 로고
    • Cycles representing the Todd class of a toric variety
    • MR2083474 (2005h:14124)
    • J. Pommersheim and H. Thomas, Cycles representing the Todd class of a toric variety, J. Amer. Math. Soc. 17 (2004), 983-994. MR2083474 (2005h:14124)
    • (2004) J. Amer. Math. Soc. , vol.17 , pp. 983-994
    • Pommersheim, J.1    Thomas, H.2
  • 24
    • 0003333144 scopus 로고
    • Convex bodies: The Brunn-Minkowski theory
    • Cambridge University Press, Cambridge. MR1216521 (94d:52007)
    • R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Encyclopedia of Mathematics and its Applications, vol. 44, Cambridge University Press, Cambridge, 1993. MR1216521 (94d:52007)
    • (1993) Encyclopedia of Mathematics and its Applications , vol.44
    • Schneider, R.1
  • 25
    • 0003690189 scopus 로고
    • Theory of linear and integer programming
    • John Wiley & Sons, Ltd., Chichester. MR0874114 (88m:90090)
    • A. Schrijver, Theory of Linear and Integer Programming, Wiley-Interscience Series in Discrete Mathematics, John Wiley & Sons, Ltd., Chichester, 1986. MR0874114 (88m:90090)
    • (1986) Wiley-interscience Series in Discrete Mathematics
    • Schrijver, A.1
  • 26
    • 79251542815 scopus 로고    scopus 로고
    • Qualitative topics in integer linear programming
    • Translated from the Russian by H. H. McFaden, American Mathematical Society, Providence, RI. MR1414900 (97m:90001)
    • V. N. Shevchenko, Qualitative Topics in Integer Linear Programming, Translated from the Russian by H. H. McFaden. Translations of Mathematical Monographs, vol. 156, American Mathematical Society, Providence, RI, 1997. MR1414900 (97m:90001)
    • (1997) Translations of Mathematical Monographs , vol.156
    • Shevchenko, V.N.1
  • 27
    • 0003306141 scopus 로고    scopus 로고
    • Enumerative combinatorics. Vol. 1
    • corrected reprint of the 1986 original. Cambridge University Press, Cambridge. MR1442260 (98a:05001)
    • R. P. Stanley, Enumerative Combinatorics. Vol. 1, corrected reprint of the 1986 original. Cambridge Studies in Advanced Mathematics, vol. 49, Cambridge University Press, Cambridge, 1997. MR1442260 (98a:05001)
    • (1997) Cambridge Studies in Advanced Mathematics , vol.49
    • Stanley, R.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.