# zbMATH — the first resource for mathematics

Sequences, groups, and number theory. (English) Zbl 1394.05002
Trends in Mathematics. Cham: Birkhäuser (ISBN 978-3-319-69151-0/hbk; 978-3-319-69152-7/ebook). xxvi, 576 p. (2018).
Publisher’s description: This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups.
This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.

The articles of this volume will be reviewed individually.
Indexed articles:
Berthé, Valérie; Rigo, Michel, General framework, 1-36 [Zbl 1407.11044]
Coons, Michael; Spiegelhofer, Lukas, Number theoretic aspects of regular sequences, 37-87 [Zbl 1423.11063]
Charlier, Émilie, First-order logic and numeration systems, 89-141 [Zbl 07006267]
Bell, Jason, Some applications of algebra to automatic sequences, 143-175 [Zbl 1425.68179]
Ochem, Pascal; Rao, Michaël; Rosenfeld, Matthieu, Avoiding or limiting regularities in words, 177-212 [Zbl 1405.05004]
Wojcik, Caïus; Zamboni, Luca Q., Coloring problems for infinite words, 213-231 [Zbl 1405.05005]
Becher, Verónica; Carton, Olivier, Normal numbers and computer science, 233-269 [Zbl 1407.11091]
Madritsch, Manfred, Normal numbers and symbolic dynamics, 271-329 [Zbl 1408.11075]
Aubrun, Nathalie; Barbieri, Sebastián; Jeandel, Emmanuel, About the domino problem for subshifts on groups, 331-389 [Zbl 1405.20023]
Klimann, Ines; Picantin, Matthieu, Automaton (semi)groups: Wang tilings and Schreier tries, 391-431 [Zbl 07006274]
Bartholdi, Laurent, Amenability of groups and $$G$$-sets, 433-544 [Zbl 07006275]

##### MSC:
 05-06 Proceedings, conferences, collections, etc. pertaining to combinatorics 20-06 Proceedings, conferences, collections, etc. pertaining to group theory 11-06 Proceedings, conferences, collections, etc. pertaining to number theory 05A05 Permutations, words, matrices 68-06 Proceedings, conferences, collections, etc. pertaining to computer science 00B15 Collections of articles of miscellaneous specific interest
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