Integer Knapsacks: Average Behavior of the Frobenius Numbers
Published Online:6 Aug 2009https://doi.org/10.1287/moor.1090.0393
References
- Hard equality constrained integer knapsacks. Math. Oper. Res. (2004) 29(3):724–738Link, Google Scholar
- An optimal lower bound for the Frobenius problem. J. Number Theory (2007) 123(1):71–79Crossref, Google Scholar
- Weak asymptotics of the numbers of solutions of Diophantine equations. Funktsionalnyi. Anal. i Prilozhen (1999) 33(4):65–66Crossref, Google Scholar
- Geometry and growth rate of Frobenius numbers of additive semigroups. Math. Phys. Anal. Geometry (2006) 9(2):95–108Crossref, Google Scholar
- Arithmetical turbulence of selfsimilar fluctuations statistics of large Frobenius numbers of additive semigroups of integers. Moscow Math. J. (2007) 7(2):173–193Crossref, Google Scholar
- Refined upper bounds for the linear Diophantine problem of Frobenius. Adv. Appl. Math. (2004) 32(3):454–467Crossref, Google Scholar
- The Frobenius problem, rational polytopes, and Fourier-Dedekind sums. J. Number Theory (2002) 96(1):1–21Google Scholar
- Faster algorithms for Frobenius numbers. Electronic J. Combin. (2005) 12(Research Paper 27), 38 (electronic). http://www.combinatorics.orgGoogle Scholar
- Limit behavior of large Frobenius numbers. Uspekhi Matematicheskikh Nauk (2007) 62(4, 376):77–90Crossref, Google Scholar
- On the linear Diophantine problem of Frobenius. J. Number Theory (1994) 48(3):353–363Crossref, Google Scholar
- Frobenius numbers by lattice point enumeration. Integers (2007) 7(15):63Google Scholar
- On a linear Diophantine problem of Frobenius. Acta Arithmetica (1972) 21:399–408Crossref, Google Scholar
- Frobenius problem and the covering radius of a lattice. Discrete Comput. Geometry (2007) 37(3):471–483Crossref, Google Scholar
- Convex and Discrete Geometry (2007) (Springer, Berlin) Google Scholar
- Geometry of Numbers (1987) (North–Holland, Amsterdam) Google Scholar
- Testing integer knapsacks for feasibility. Eur. J. Oper. Res. (1996) 88(3):578–582Crossref, Google Scholar
- Lattice translates of a polytope and the Frobenius problem. Combinatorica (1992) 12(2):161–177Crossref, Google Scholar
- Covering minima and lattice-point-free convex bodies. Ann. Math. (2) (1988) 128(3):577–602Crossref, Google Scholar
- , Miller R. E., Thatcher J. W. Reducibility among combinatorial problems. Complexity of Computer Computations (1972) (Plenum, New York) 85–103Crossref, Google Scholar
- , Goldberg A., Zhou Y. Nonlinear optimization over a weighted independence system. Proc. 2009 AAIM (2009) 5564(Springer, Berlin) 251–264LNCSCrossref, Google Scholar
- The asymptotic distribution of Frobenius numbers. (2009) . arXiv.org. arXiv:0902.3557Google Scholar
- Complexity of the Frobenius problem. Combinatorica (1996) 16(1):143–147Crossref, Google Scholar
- The Diophantine Frobenius problem. Oxford Lecture Series in Mathematics and Its Applications (2005) (Oxford University Press, Oxford, UK) Crossref, Google Scholar
- An estimate for Frobenius' Diophantine problem in three dimensions. J. Integer Sequences (2005) 8(1, Article 05.1.7) 4 (electronic). http://www.cs.uwaterloo.ca/journals/JISGoogle Scholar
- The distribution of sublattices of Zm. Monatshefte Math. (1998) 125(1):37–81Crossref, Google Scholar
- On the linear Diophantine problem of Frobenius. J. Reine Angewandte Math. (1977) 293/294:1–17Google Scholar
- Limiting distribution of Frobenius numbers for n = 3. (2009) . arXiv.org. arXiv:0810.5219v1Google Scholar
- On the distribution of Frobenius numbers with three arguments I. Mat. Sb. (2009) . ForthcomingCrossref, Google Scholar
- Bounds for a linear Diophantine problem of Frobenius. J. London Math. Soc. (1975) 10(2):79–85Crossref, Google Scholar

