CARMA OANT SEMINAR Speaker: Yohei Tachiya, Graduate School of Science and Technology, Hirosaki University Title: Algebraic independence results for the generating functions of pattern sequences Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 4:00 pm, Mon, 27th Oct 2014 SeeVogh meeting 3144213387. Abstract: We first introduce the notations of pattern sequence, which is defined by the number of (possibly) overlapping occurrences of a given word in the $\langle q,r\rangle$-numeration system. After surveying several properties of pattern sequence, we will give necessary and sufficient criteria for the algebraic independence of their generating functions. As applications, we deduce the linear relations between pattern sequences. The proofs of the theorem and the corollaries are based on Mahler's method. [Permanent link]