# Set Partitions, Tableaux, and Subspace Profiles under Regular Split Semisimple Matrices

### Samrith Ram (IIIT Delhi)

03-Feb-2022, 08:30-09:30 (14 months ago)

Abstract: In this talk we will introduce a family of polynomials $b_\lambda(q)$ indexed by integer partitions $\lambda$. These polynomials arise from an intriguing connection between two classical combinatorial classes, namely set partitions and standard tableaux. The polynomials $b_\lambda(q)$ can be derived from a new statistic on set partitions called the interlacing number which is a variant of the well-known crossing number of a set partition. These polynomials also have several interesting specializations: $b_\lambda(1)$ enumerates the number of set partitions of shape $\lambda$ and $b_\lambda(0)$ counts the number of standard tableaux of shape $\lambda$ while $b_\lambda(-1)$ equals the number of standard shifted tableaux of shape $\lambda$ respectively. When $q$ is a prime power $b_\lambda(q)$ counts (up to factors of $q$ and $q-1$) the number of subspaces in a finite vector space that transform under a regular diagonal matrix in a specified manner.

This is joint work with Amritanshu Prasad.

combinatorics

Audience: researchers in the topic

( paper | video )

Series comments: Timings may vary depending on the time zone of the speakers.

 Organizers: Amritanshu Prasad*, Apoorva Khare*, Pooja Singla*, R. Venkatesh* *contact for this listing

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