Generating function for K-restricted jagged partitions
Fortin, J. -F. ; Jacob, P. ; Mathieu, P.
arXiv, 0305055 / Harvested from arXiv
Text on arXiv
We present a natural extension of Andrews' multiple sums counting partitions with difference 2 at distance $k-1$, by deriving the generating function for $K$-restricted jagged partitions. A jagged partition is a collection of non-negative integers $(n_1,n_2,..., n_m)$ with $n_m\geq 1$ subject to the weakly decreasing conditions $n_i\geq n_{i+1}-1$ and $n_i\geq n_{i+2}$. The $K$-restriction refers to the following additional conditions: $n_i \geq n_{i+K-1} +1$ or $ n_i = n_{i+1}-1 = n_{i+K-2}+1= n_{i+K-1}$. The corresponding generalization of the Rogers-Ramunjan identities is displayed, together with a novel combinatorial interpretation.
Publié le : 2003-05-26
Classification:  Mathematical Physics,  Mathematics - Combinatorics 
@article{0305055,
     author = {Fortin, J. -F. and Jacob, P. and Mathieu, P.},
     title = {Generating function for K-restricted jagged partitions},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0305055}
}

Fortin, J. -F.; Jacob, P.; Mathieu, P. Generating function for K-restricted jagged partitions. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0305055/