The splitting subspace conjecture. (English) Zbl 1286.05007
Summary: We answer a question of Niederreiter concerning the enumeration of a class of subspaces of finite-dimensional vector spaces over finite fields by proving a conjecture of S. R. Ghorpade and S. Ram [ibid. 17, No. 5, 461–472 (2011; Zbl 1263.11112)].
MSC:
| 05A15 | Exact enumeration problems, generating functions |
| 11T71 | Algebraic coding theory; cryptography (number-theoretic aspects) |
| 15A03 | Vector spaces, linear dependence, rank, lineability |
Keywords:
finite fields; splitting subspaces; finite-dimensional vector spaces; \(q\)-Chu-Vandermonde identity; enumerationCitations:
Zbl 1263.11112References:
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| [3] | Ghorpade, S. R.; Ram, S., Block companion Singer cycles, primitive recursive vector sequences, and coprime polynomial pairs over finite fields, Finite Fields Appl., 17, 461-472 (2011) · Zbl 1263.11112 |
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