Linear relations between pattern sequences in a 〈q,r〉-numeration system

Authors: Shiokawa, I.¹; Tachiya, Y.²

Source: Acta Mathematica Hungarica, Volume 132, Numbers 1-2, July 2011 , pp. 190-206(17)

Publisher: Springer

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Abstract:

We investigate linear relations between pattern sequences in a 〈q,r〉-numeration system, and give a basis of the module generated by pattern sequences for words of length not exceeding l. The expressions of pattern sequences using the basis are also studied. Similar results are obtained for the module generated by all pattern sequences.

Keywords: pattern sequence; block counting; digit; 〈q,r〉-numeration system; positional number system; algebraic independence; 11A63; 11J81; 11J85

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10474-011-0082-6

Affiliations: 1: Department of Mathematics, Keio University, Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan, Email: shiokawa@math.keio.ac.jp 2: Department of Mathematics, Keio University, Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan, Email: bof@math.keio.ac.jp

Publication date: 2011-07-01