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SUMMARY:Samrith Ram (IIIT Delhi)
DTSTART;VALUE=DATE-TIME:20220203T083000Z
DTEND;VALUE=DATE-TIME:20220203T093000Z
DTSTAMP;VALUE=DATE-TIME:20240224T052339Z
UID:ARCSIN/13
DESCRIPTION:Title:
Set Partitions\, Tableaux\, and Subspace Profiles under Regular Split Semi
simple Matrices\nby Samrith Ram (IIIT Delhi) as part of ARCSIN - Algeb
ra\, Representations\, Combinatorics and Symmetric functions in INdia\n\n\
nAbstract\nIn this talk we will introduce a family of polynomials $b_\\lam
bda(q)$ 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 inte
rlacing number which is a variant of the well-known crossing number of a s
et partition. These polynomials also have several interesting specializati
ons: $b_\\lambda(1)$ enumerates the number of set partitions of shape $\\
lambda$ and $b_\\lambda(0)$ counts the number of standard tableaux of shap
e $\\lambda$ 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 i
n a specified manner.\n\nThis is joint work with Amritanshu Prasad.\n
LOCATION:https://researchseminars.org/talk/ARCSIN/13/
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