Affiliation: Laval University, Quebec
Email: pmathieu@phy.ulaval.ca
Title Of Talk: Summing `jagged partitions' with exclusion
URL: jagged.pdf
Abstract: By `jagged partitions' we refer to a collection of non-negative integers $(n_1,n_2,\cdots , n_m)$ 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 exclusion refers to the following difference condition: $n_i \geq n_{i+K-1} +1$ or $ n_i = n_{i+K-1} $ and $n_{i+1} = n_{i+K-2}+2$. We present their generating fucntion. It is a rather direct generalization of that of partitions $(\la_1,\la_2,\cdots , \la_m)$ subject to the difference condition $\la_i\geq \la_{i+k-1}+2$ found by Andrews. These restricted partitions arise in the following physical context: for $K=2k$, they describe the quasi-particle basis of a two-dimensional conformal field theory, namely the graded parafermionic theory with $\Z_{2k}$ cylic symmetry.
Last update made Wed Mar 26 16:39:44 EST 2003.
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