The Splitting Subspace Conjecture

Abstract

We answer a question by Niederreiter concerning the enumeration of a class of subspaces of finite dimensional vector spaces over finite fields by proving a conjecture by Ghorpade and Ram.

12 pages, Corrected factor of (1-q) in L=R expression in proof of Theorem 3.3

References in corpus (2)

• Primitive Polynomials, Singer Cycles, and Word-Oriented Linear Feedback Shift Registers
• Block Companion Singer Cycles, Primitive Recursive Vector Sequences, and Coprime Polynomial Pairs over Finite Fields

Cited by in corpus (10)

• A note on the multiple-recursive matrix method for generating pseudorandom vectors
• An asymptotic formula for the number of irreducible transformation shift registers
• Absolute order in general linear groups
• Enumeration of Linear Transformation Shift Registers
• Splitting subspaces and a finite field interpretation of the Touchard-Riordan Formula
• Set partitions, tableaux, and subspace profiles under regular diagonal matrices
• Enumeration of Anti-Invariant Subspaces and Touchard's Formula for the Entries of the $q$-Hermite Catalan Matrix
• Subspace Profiles over Finite Fields and $q$-Whittaker Expansions of Symmetric Functions
• Primitive transformation shift registers over finite fields
• Primitive transformation shift registers of order two over fields of characteristic two