Some generating functions
About: This article is published in Duke Mathematical Journal. The article was published on 01 Jun 1963. and is currently open access.
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Citations
On Pairs of Partitions with Steadily Decreasing Parts Communicated by George Andrews
TL;DR: A new generating function identity for special pairs of partitions with steadily decreasing parts is proved via a bijection via coloured modular Young diagrams.
16
The clustering of disease
TL;DR: A new mathematical rationale for epidemic processes is introduced, and a convenient framework for describing disease clusters is provided, which is used to describe a new epidemic pattern of type-A hepatitis.
14
Infinite products over visible lattice points
TL;DR: In this paper, fifty new multivariate combinatorial identities are given, connected with partition theory, prime products, and Dirichlet series, and connections to Lattice Sums in Chemistry and Physics are alluded to also.
Partitions of bi-partite numbers into at mostj parts
TL;DR: The number of partitions of a bi-partite number into at mostj parts is studied and it is shown that this function is maximized whenx=y, and an explicit formula fornj is provided so that, for alln≥nj, x=y yields a maximum forpj(x,y).
5
An extension of Carlitz’s bipartition identity
George E. Andrews
- 01 Jan 1977
TL;DR: In this paper, the bipartition identity is extended to a multipartite partition identity by the introduction of the summatory maximum function: smax(n 1,n 2. n) = nl + n2 + + n, (r l)min(nl,n2,.n).
References
•Book
Generalized Hypergeometric Series
Wilfrid Norman Bailey
- 01 Jul 1965
TL;DR: Koornwinder as discussed by the authors gave identitity (2.5) with N = 0 and formulas (5.3), 5.3, and 5.4) substituted.
1.9K
•Book
The Theory of Equations: With an Introduction to the Theory of Binary Algebraic Forms
William Snow Burnside
- 27 Jan 2005
TL;DR: The theory of substitutions and groups was introduced by Panton in this paper, where the authors give just so much of the elementary theory of substitution-groups as to enable them to prove the fundamental property of the Galoisian resolvent of an equation, and to demonstrate that the general equation of any degree higher than the fourth cannot be solved by an algebraic formula.
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