The existence of a cyclic sieving phenomenon for permutations via a bound on the number of border strip tableaux and invariant theory

12.11.2019 15:15 - 16:45

Martin Rubey (TU Wien)


We consider permutations pi of {1,...,n} as chord diagrams, where the elements label the vertices of a regular n-gon, and there is a directed arc from i to pi(i) for each element i. We can "rotate" a permutation by rotating its chord diagram.

As one of our main results we show that there must exist a statistic on permutations of {1,...,n} that has the same distribution as the length of the longest increasing subsequence, but is invariant under rotation.

The proof uses a little combinatorial representation and invariant theory, and some calculus. It appears non-trivial to exhibit the statistic explicitly.

The main motivation of a two-element subset of the authors is to find a "web" basis (in the sense of Kuperberg) for the adjoint representation of the general linear group.

This is joint work with Per Alexandersson, Stephan Pfannerer & Joakim Uhlin.


M. Drmota

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