Mathematics Colloquia and Seminars

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Description

Let s\leq t be relatively prime. There is a beautiful bijection between 'Dyck paths' in the s-by-t rectangle and partitions with no hook lengths equal to s or t (simultaneous cores). Thanks to the bijection, there is a nice enumeration of these cores. Recently, Armstrong, Hanusa and Jones have made some progress on q-enumerating these cores; there is a conjectured q-statistic which was proven in the case where s=1 or 2. We present this background, future directions, and some really nice combinatorics.

Note: special day!