Daniel Dombek - publications, presentations 1 Publications

Daniel Dombek - publications, presentations
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Publications
Articles in peer-reviewed journals:
D. Dombek, Z. Masáková, V. Ziegler, Distinct unit generated totally complex quartic
fields, J. Number Theor. 148: 311–327. (2015) doi:10.1016/j.jnt.2014.09.029
D. Dombek, L. Hajdu, A. Pethő, Representing algebraic integers as linear combinations
of units, Period. Math. Hungar. 68(2): 135–142. (2014) doi:10.1007/s10998-014-0020-9
D. Dombek, Substitutions over infinite alphabet generating (−β)-integers, Int. J. Found.
Comput. Sci. 23(8): 1627–1639. (2012) doi:10.1142/S0129054112400667
P. Ambrož, D. Dombek, Z. Masáková, E. Pelantová, Numbers with integer expansion
in the numeration system with negative base, Funct. Approx. Comment. Math 47(2):
241–266. (2012) doi:10.7169/facm/2012.47.2.8
D. Dombek, Z. Masáková, E. Pelantová, Number representation using generalized (−β)transformation, Theor. Comput. Sci. 412(48): 6653–6665. (2011)
doi:10.1016/j.tcs.2011.08.028
Preprints:
D. Dombek, Z. Masáková, T. Vávra, Confluent Parry numbers, their spectra, and integers
in positive- and negative-base number systems, to appear in J. Théor. Nombres Bordeaux
(2015) arXiv:1402.4314
Contributions in conference proceedings:
D. Dombek, Generating (±β)-integers by Conjugated Morphisms, Local Proceedings of
WORDS 2013, TUCS Lecture Notes 20: 14–25. (2014)
D. Dombek, On the generalizations of the unit sum number problem, Doktorandské dny
2012, Česká technika - nakladatelství ČVUT, 15–19. (2011)
D. Dombek, Substitutions over infinite alphabet generating (−β)-integers, Proceedings
of WORDS 2011, EPTCS 63: 115–121. (2011)
D. Dombek, Antimorphisms generating (−β)-integers, Doktorandské dny 2011, Česká
technika - nakladatelství ČVUT, 25–29. (2011)
P. Ambrož, D. Dombek, Z. Masáková, E. Pelantová, Numbers with integer expansions
in the numeration system with negative base, Proceedings of the 13th Mons Theoretical
Computer Days, Amiens, U.F.R. Sciences 1–8. (2010)
Student theses:
D. Dombek, Non-standard representations of numbers, Doctoral thesis, ČVUT v Praze
(2014)
D. Dombek, Beta-numeration systems with negative bases, Master thesis, ČVUT v Praze
(2010)
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D. Dombek, Aritmetika kvadratických beta-celých čísel, Research project, ČVUT v Praze
(2009)
D. Dombek, Poziční numerační systémy s rozšířenou abecedou, Bachelor thesis, ČVUT
v Praze (2008)
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Presentations
Attended conferences, invited lectures:
July 2014, Debrecen (Hungary), Numeration and Substitution 2014, lecture: On distinct
unit generated fields that are totally complex
September 2013, Turku (Finland), WORDS 2013, lecture: On the characterization of all
β with (±β)-integers encoded by conjugated morphisms
July 2013, Grenoble (France), 28th Journées Arithmétiques, lecture: On the characterization of all β with (±β)-integers encoded by conjugated morphisms
November 2012, Graz (Austria), Technical University of Graz, invited lecture: On the
generalizations of the unit sum number problem
October 2012, Ostrava (Czech Rep.), 6th PhD Student Mathematical Conference, lecture: On the generalizations of the unit sum number problem
September 2012, Telč (Czech Rep.), Česko-Slovenská MELA - Meeting on Languages,
lecture: Integers in numeration systems with irrational bases
May 2012, Marseille (France), School on Combinatorics, Automata and Number Theory
CANT, poster: Algebraic integers as combinations of units
May 2012, Malenovice (Czech Rep.), ISCAMI 2012, lecture: On the generalizations of
the unit sum number problem
October 2011, Matematický ústav, Univerzita Debrecen (Hungary), invited lecture: Numeration systems with negative base
September 2011, Praha (Czech Rep.), WORDS 2011, lecture: Substitutions over infinite
alphabet generating (−β)-integers
June 2011, Vilnius (Lithuania), 27th Journées Arithmétiques, lecture: Numeration systems with negative base
June 2011, Liège (Belgium), Numération 2011, lecture: Expansions of numbers in a
negative base
March 2011, Villa Lanna, Praha (Czech Rep.), Analytic and algebraic methods VIII,
lecture: Generalised numeration systems with negative base
September 2010, Fakulta informatiky, Univerzita Debrecen (Hungary), invited lecture:
Numeration systems with negative base
May 2010, Villa Lanna, Praha (Czech Rep.), Analytic and algebraic methods VII, lecture:
Numbers with integer expansion in the numeration system with negative base
January 2010, Horní Polubný (Czech Rep.), The 19th Student Winter School on Mathematical physics, lecture: Non-standard numeration systems I
June 2009, Leiden (Netherlands), Numeration, student conference and workshop
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Other presentations:
May 2014, Kruh u Jilemnice (Czech Rep.), Combinatorics on Words and Mathematical
Physics 2014, student workshop, lecture: Kódování množin celých čísel v soustavách s
kladnou a zápornou bází
May 2013, Dolní Lomná (Czech Rep.), Combinatorics on Words and Mathematical
Physics 2013, student workshop, lecture: Izomorfsmy mezi β- a (−β)-tranformacemi
November 2012, Praha (Czech Rep.), workshop Doktorandské dny at KM FJFI ČVUT,
lecture: On the generalizations of the unit sum number problem
May 2012, Svatý Jan pod Skalou (Czech Rep.), Combinatorics on Words and Mathematical Physics 2012, student workshop, lecture: Classical proofs from number theory
March 2012, Praha (Czech Rep.), Combinatorial and Algebraic Structures Seminar, FJFI
ČVUT v Praze, lecture: On the generalizations of the unit sum number problem
March 2012, Praha (Czech Rep.), Combinatorial and Algebraic Structures Seminar, FJFI
ČVUT v Praze, lecture: Random graphs – Graph theory meeting probability with asymptotics
May 2011, Vlachovice (Czech Rep.), Combinatorics on Words 2011, student workshop,
lecture: Equations on words
May 2010, Hojsova Stráž (Czech Rep.), Combinatorics on Words 2010, student workshop,
lecture: Minimal expansions in redundant number systems
June 2009, Děčín (Czech Rep.), Combinatorics on Words 2009, student workshop, lecture: Aritmetika v kvadratických Pisot soustavách
August 2008, Telč (Czech Rep.), Algebraic Structures 2008, student workshop, lecture:
Poziční numerační systémy s rozšířenou abecedou
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