On new modulo 8 cylindric partition identities.

 

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Abstract: We will discuss new sum-product identities that emerged from the study of cylindric partitions. Cylindric partitions were defined by Gessel and Krattenthaler in 1997 in the context of non-intersecting lattice paths. These combinatorial objects later appeared naturally in many different contexts. Most recently, Corteel and Welsh re-derived the A2 Rogers-Ramanujan identities originally proven by Andrews, Schilling and Warnaar using cylindric partitions. In this study they proved a general recurrence relation for cylindric partitions which can be applied to any class of such partitions. In a joint effort, the speaker, Corteel and Dousse studied a different class of cylindric partitions. This study lead to many intriguing multisum-product identities where the product side has a modulo 8 structure.