A new proof of the Bender-Coley-Robbins-Rumsey formula for subspace profiles uses double counting with partial linear maps over finite fields, yielding Niederreiter's splitting subspace count as a corollary.
Splitting subspaces of linear operator s over finite fields
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Simple operators and $q$-Whittaker coefficients of power sum symmetric functions
A new proof of the Bender-Coley-Robbins-Rumsey formula for subspace profiles uses double counting with partial linear maps over finite fields, yielding Niederreiter's splitting subspace count as a corollary.