Lehr (1991) proved that, if M(q, r) denotes the set of real numbers whose expansion in base-r is q-automatic i.e., is recognized by an automaton A = (Aq, Ar, ao, δ, φ) (or is the image under a letter to letter morphism of a fixed point of a substitution of constant length q) then M(q, r) is closed under addition and rational multiplication. Similarly if we let M(r) denote the set of real numbers α whose base-r digit expansion is ultimately primitive substitutive, i.e., contains a tail which is the image (under a letter to letter morphism) of a fixed point of a primitive substitution then in an attempt to generalize Lehr's result we show that the set M(r) is closed under multiplication by rational numbers. We also show that M(r) is not closed under addition.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc278637 |
| Date | 08 1900 |
| Creators | Ketkar, Pallavi S. (Pallavi Subhash) |
| Contributors | Zamboni, Luca Quardo, 1962-, Bator, Elizabeth M., Iaia, Joseph A. |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iv, 17 leaves, Text |
| Rights | Public, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved., Ketkar, Pallavi S. (Pallavi Subhash) |
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