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SUMMARY:Samrith Ram (IIIT Delhi)
DTSTART:20220203T083000Z
DTEND:20220203T093000Z
DTSTAMP:20260423T004659Z
UID:ARCSIN/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ARCSIN/13/">
 Set Partitions\, Tableaux\, and Subspace Profiles under Regular Split Semi
 simple Matrices</a>\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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