Jagged partitions

Details Jagged partitions Jagged partitions

2003-10-06

arxiv.org/abs/math/0310079v2

Ramanujan Journal 10 (2005) 215-235

Mathematics

Combinatorics

17 pages (Latex). The revised version includes few corrections, a comment concerning the identity of app. A and a note added.

Scientific paper

By jagged partitions we refer to an ordered collection of non-negative integers $(n_1,n_2,..., n_m)$ with $n_m\geq p$ 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 $n_i\geq n_{i+1}-1$ and $n_i\geq n_{i+2}$. 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.

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