Jagged Partitions |
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| Authors: | Email author" target="_blank">J-F?FortinEmail author P?Jacob P?Mathieu |
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| Institution: | (1) Département de physique, de génie physique et d'optique, Université Laval, Québec, Canada, G1K 7P4;(2) Present address: Department of Physics and Astronomy, Rutgers, The State University of New Jersey, Piscataway, NJ, 08854-8019;(3) Present address: Department of Mathematical Sciences, University of Durham, Durham, DH1 3L, UK |
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| Abstract: | By jagged partitions we refer to an ordered collection of non-negative integers (n1, n2,..., nm) with nm≥ p for some positive integer p, further subject to some weakly decreasing conditions that prevent them for being genuine partitions. The case analyzed in
greater detail here corresponds to p = 1 and the following conditions ni≥ ni+1−1 and ni≥ ni+2. A number of properties for the corresponding partition function are derived, including rather remarkable congruence relations.
An interesting application of jagged partitions concerns the derivation of generating functions for enumerating partitions
with special restrictions, a point that is illustrated with various examples.
2000 Mathematics Subject Classification: Primary—05A15, 05A17, 05A19 |
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| Keywords: | partitions generating functions congruence relations |
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