### Wednesday, July 15

## MS19

Number Theory and Formal Languages

10:30 AM-12:30 PM

*Room: Sidney Smith 1072*

Arithmetic properties of real numbers or of formal power series can often be deduced from combinatorial properties of the infinite sequences of their digits or coefficients. The speakers will illustrate these links between discrete combinatorial properties of sequences, number theory, and language theory, in four directions: combinatorial properties of 2-dimensional sequences that are periodic in one direction, computation of the i-th digit of the n-th iterated image of a morphism, arithmetic properties of real numbers generated by primitive morphisms, transcendence of numbers having a "combinatorially good" base-r or continued fraction expansion.

**Organizer: Jean-Paul S. Allouche**

*CNRS, Université Paris-Sud Orsay, France*
**10:30 On Bidimensional Sequences**
- Michel Koskas, LARIA, Université d'Amiens, France
**11:00 A Polynomial Time Algorithm for Computing the ***i*'th Digit of varphi ^{n} *(a)*
- Jeff Shallit, and
*David Swart*, University of Waterloo, Canada
**11:30 Real Numbers Whose Base *** r* Expansion is Given by a Substitution
- Luca Q. Zamboni, University of North Texas
**12:00 Transcendence of Real Numbers Whose Binary or Continued Fraction Expansion is a Fixed Point of a Morphism**
- Jean-Paul Allouche, Organizer

*LMH, 2/23/98; MMD, 6/17/98*