Abstract:
In this lecture, we are going to explore some intricate connections between cranks and frobenius symbols for integer partitions. One of the most charming results in the elementary theory of partitions is the Stanley–Elder theorem. Our object in this paper is to prove a very similar theorem relating the cranks of partitions to the Frobenius symbols for partitions. The surprise of such a result lies in the fact that cranks seemingly have been historically unrelated to Frobenius symbols; indeed, it would be an ominous task to define the crank based on the related Frobenius symbol. This result can be a starting point for a new combinatorial investigation into both topics.
Stanley-Elder theorem with a twist
20.06.2023 15:15 - 16:45
Organiser:
M. Drmota
Location: