zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Five guidelines for partition analysis with applications to lecture hall-type theorems. (English) Zbl 1182.11049
Landman, Bruce (ed.) et al., Combinatorial number theory. Proceedings of the 2nd integers conference 2005 in celebration of the 70th birthday of Ronald Graham, Carrollton, GA, USA, October 27–30, 2005. Berlin: Walter de Gruyter (ISBN 978-3-11-019029-8/hbk). 131-155 (2007) and Integers 7, No. 2, Paper A9 (2007).
This investigation continues the authors’ earlier work [Ramanujan J. 8, No. 3, 357–381 (2004; Zbl 1071.05007)] on nonnegative integer solutions to linear inequalities as they relate to enumeration of integer partitions and compositions. Five guidelines are developed to compute the generating function for the solutions, using an approach that emphasizes deriving recurrences. In their previous papers they used an invertible matrix C that handled the cases of Hickerson partitions, partitions with rth differences nonnegative, and various others. For some cases this “C-matrix” approach fails, so here they develop the guidelines to derive a recurrence for the generating function of an infinite family of constraint systems. This is applied to the problem of enumerating anti-lecture hall compositions [Discrete Math. 263, No. 1–3, 275–280 (2003; Zbl 1019.05004)] and truncated lecture-hall partitions [J. Comb. Theory, Ser. A 108, No. 2, 217–245 (2004; Zbl 1061.05009)]. These methods are seen to be preferable to other work involving q-series. Finally, the authors point out how their guidelines relate to McMahon’s partition analysis.
MSC:
11P81Elementary theory of partitions
05A17Partitions of integers (combinatorics)