The Splitting Subspace Conjecture

TL;DR

This paper proves a conjecture related to counting specific subspaces in finite-dimensional vector spaces over finite fields, addressing a question posed by Niederreiter.

Contribution

It provides a proof of the Splitting Subspace Conjecture, resolving an open problem in finite field subspace enumeration.

Findings

Confirmed the conjecture by Ghorpade and Ram

Established a new enumeration formula for splitting subspaces

Resolved Niederreiter's question on subspace counting

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.