SL2(k) and a Subset of Words Overk

Given a field k, this paper defines a subset of the free semi-groupFk (whose elements are all finite words with letters in k) which has some interesting arithmetic and combinatorial properties. The case p = 2 has been treated in Bacher (2000, Europ. J. Combinatorics, 21, 853–864) with slightly different notations. The link withSL2 and motivation for studying this subset originates in Bacher (1999, Ann. Inst. Fourier, 49, 1115–1128).