论文信息 - Partition identities and the coin exchange problem

Partition identities and the coin exchange problem

The number of partitions of n into parts divisible by a or b equals the number of partitions of n in which each part and each difference of two parts is expressible as a non-negative integer combination of a and b. This generalizes identities of MacMahon and Andrews. The analogous identities for three or more integers (in place of a,b) hold in certain cases.

Alexander E. Holroyd

[1] George E. Andrews,et al. Integrals, partitions and MacMahon's Theorem , 2007, J. Comb. Theory, Ser. A.

[2] Ramírez Alfonsin,et al. The diophantine frobenius problem , 2005 .

[3] George E. Andrews,et al. An algebraic identity of F.H. Jackson and its implications for partitions , 2001, Discret. Math..

[4] Emil Grosswald,et al. The Theory of Partitions , 1984 .

[5] Graham C. Denham,et al. Short Generating Functions for some Semigroup Algebras , 2003, Electron. J. Comb..

[6] Partitions with short sequences and mock theta functions. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[7] Dan Romik,et al. Integrals, partitions, and cellular automata , 2003 .

[8] László A. Székely,et al. Generating functions for the Frobenius Problem with 2 and 3 generators , 1986 .

[9] J. J. Sylvester,et al. On Subvariants, i.e. Semi-Invariants to Binary Quantics of an Unlimited Order , 1882 .

[10] Herbert S. Wilf,et al. Representations of integers by linear forms in nonnegative integers , 1972 .

[11] George E. Andrews. A generalization of a partition theorem of MacMahon , 1967 .