The Splitting Subspace Conjecture
arXiv:1208.0851 · doi:10.1016/j.ffa.2013.05.006
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
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- Enumeration of Linear Transformation Shift Registers
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- Set partitions, tableaux, and subspace profiles under regular diagonal matrices
- Enumeration of Anti-Invariant Subspaces and Touchard's Formula for the Entries of the -Hermite Catalan Matrix
- Subspace Profiles over Finite Fields and -Whittaker Expansions of Symmetric Functions
- Primitive transformation shift registers over finite fields
- Primitive transformation shift registers of order two over fields of characteristic two