arXiv math/03100792003-10math.COmath-phmath.MP

Jagged partitions

J. -F. Fortin, P. Jacob, P. Mathieu

备注：: 17 pages (Latex). The revised version includes few corrections, a comment concerning the identity of app. A and a note added. To appear in Ramanujan Journal
发表信息：: Ramanujan Journal 10 (2005) 215-235

英文摘要：

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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