论文信息 - Some variants of Ferrers diagrams

Some variants of Ferrers diagrams

Abstract In this paper, we consider variants of Ferrers diagrams in which the underlying square grid is replaced by other regular patterns in the plane. These diagrams turn out to be related to classical identities of Euler, Sylvester, Glaisher, and MacMahon, as well as more recent results of Gollnitz, Gordon, and Andrews. Other identities appear to be new.

James Propp

[1] G. Hardy,et al. An Introduction to the Theory of Numbers , 1938 .

[2] A. Walfisz. Zur additiven Zahlentheorie , 1935 .

[3] George E. Andrews,et al. A generalization of the Göllnitz-Gordon partition theorems , 1967 .

[4] Basil Gordon. Some continued fractions of the Rogers-Ramanujan type , 1965 .

[5] George E. Andrews,et al. Generalized Frobenius Partitions , 1984 .

[6] Verallgemeinerte Partitionsfunktionen. Partitionen mit Differenzenbedingungen. , 1967 .

[7] R. Stanley. Ordered Structures And Partitions , 1972 .

[8] Lucy Joan Slater,et al. Further Identities of the Rogers‐Ramanujan Type , 1952 .

[9] G. Meinardus,et al. Über Partitionen mit Differenzenbedingungen , 1954 .

[10] L. Euler. Introductio in analysin infinitorum , 1967 .

[11] J. J. Sylvester,et al. A Constructive Theory of Partitions, Arranged in Three Acts, an Interact and an Exodion , 1882 .

[12] G. Andrews. The Theory of Partitions: Frontmatter , 1976 .