51 citations · 293 across the 47 of their papers we have counts for
48 papers
On the Existence of Elementwise Invariant Vectors in Representations of Symmetric Groups
Amrutha P, Amritanshu Prasad, Velmurugan S
We determine when a permutation with cycle type admits a non-zero invariant vector in the irreducible representation of the symmetric group. We find that a majority of pa…
Representation zeta functions of groups of type in positive characteristic
Uri Onn, Amritanshu Prasad, Pooja Singla
We prove two conjectures regarding the representation growth of groups of type . The first, conjectured by Avni, Klopsch, Onn and Voll, regards the uniformity of representatio…
Enumeration of Anti-Invariant Subspaces and Touchard's Formula for the Entries of the -Hermite Catalan Matrix
Amritanshu Prasad, Samrith Ram
We express the number of anti-invariant subspaces for a linear operator on a finite vector space in terms of the number of its invariant subspaces. When the operator is diagonaliza…
Some Restriction Coefficients for the Trivial and Sign Representations
Sridhar P. Narayanan, Digjoy Paul, Amritanshu Prasad +1
We use character polynomials to obtain a positive combinatorial interpretation of the multiplicity of the sign representation in irreducible polynomial representations of $GL_n(\ma…
Splitting subspaces and a finite field interpretation of the Touchard-Riordan Formula
Amritanshu Prasad, Samrith Ram
We enumerate the number of -splitting subspaces of dimension for an arbitrary operator on a -dimensional vector space over a finite field. When is regular split…
Simultaneous Conjugacy Classes of Finite -groups of rank
Dilpreet Kaur, Sunil Kumar Prajapati, Amritanshu Prasad
For a finite group , we consider the problem of counting simultaneous conjugacy classes of -tuples and simultaneous conjugacy classes of commuting -tuples in . Let $α_{…