Generating functions and duality for integer programs

Aardal, 2002, Non-standard approaches to integer programming, Discrete Appl. Math., 123, 5, 10.1016/S0166-218X(01)00337-7 Alekseevskaya, 1988, An arrangement of real hyperplanes and the partition function connected with it, Soviet Math. Dokl., 36, 589 Barvinok, 1999, An algorithmic theory of lattice points in polyhedra, 91 Blair, 1982, The value function of an integer program, Math. Programming, 23, 237, 10.1007/BF01583794 Brion, 1997, Residue formulae, vector partition functions and lattice points in rational polytopes, J. Amer. Math. Soc., 10, 797, 10.1090/S0894-0347-97-00242-7 Chen, 2002, Lattice points, Dedekind sums, and Ehrhart polynomials of lattice polyhedra, Discrete Comput. Geom., 28, 175, 10.1007/s00454-002-2759-7 P. Conti, C. Traverso, Buchberger algorithm and integer programming, in: F.F. Mattson, T. Mora, T.R.N. Rao (Eds.), Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Lecture Notes in Computer Science, Vol. 539, Springer, Berlin, 1991, pp. 130–139. Gomory, 1969, Some polyhedra related to combinatorial problems, Linear Algebra Appl., 2, 451, 10.1016/0024-3795(69)90017-2 S. Hosten, R. Thomas, Groebner bases and integer programming, in: B. Buchberger, F. Winkler (Eds.), Groebner Bases and Applications, Proceedings of 33 Years of Groebner Bases Conference, London Mathematical Society Lecture Note Series 251, Cambridge University Press, Cambridge, 1998, pp. 144–158. Hosten, 2003, Gomory integer programs, Math. Programming, 96B, 271, 10.1007/s10107-003-0386-6 Lasserre, 2002, La valeur optimale des programmes entiers, C.R. Acad. Sci. Paris Ser. I, 353, 863, 10.1016/S1631-073X(02)02591-8 Lasserre, 2004, Duality and a Farkas lemma for integer programs Nemhauser, 1985, Duality for integer optimization Nemhauser, 1988 Pukhlikov, 1993, A Riemann–Roch theorem for integrals and sums of quasipolynomials over virtual polytopes, St. Petersburg Math. J., 4, 789 Schrijver, 1986 Sturmfels, 1997, Variation of cost functions in integer programming, Math. Programming, 77, 357, 10.1007/BF02614622 Thomas, 1995, A geometric Buchberger algorithm for integer programming, Math. Oper. Res., 20, 864, 10.1287/moor.20.4.864 Thomas, 2001, Algebraic methods in integer programming Wolsey, 1971, Extensions of the group theoretic approach in integer programming, Management Sci., 18, 74, 10.1287/mnsc.18.1.74 Wolsey, 1981, Integer programming duality, Math. Programming, 20, 173, 10.1007/BF01589344