Research

(note that the links to arXiv or to pdf files are links to preprints that sometimes significantly differ from the published versions)

• Twin Towers of Hanoi
  accepted in European Journal of Combinatorics
  arXiv, journal,


• Cayley automatic groups are not necessarily Cayley biautomatic
  accepted in Lecture Notes in Computer Science
  with A. Miasnikov
  arXiv,


• On groups whose geodesic growth is polynomial
  accepted in International Journal of Algebra and Computation
  with M. Bridson, J. Burillo, M. Elder
  arXiv, journal,


• Pattern closure in groups of tree automorphisms
  Buletin of Mathematical Sciences 1 (2011) 1, 115--127
  arXiv, journal, paper


• Normal art galleries: wall in - all in
  arXiv


• The conjugacy problem is not solvable in automaton groups
  with Enric Ventura
  arXiv,


• Finite self-similar p-groups with abelian first level stablizers
  International Journal of Algebra and Computation 21 (2011) 1-2, 355--364.
  arXiv, journal, paper


• Polynomial functions on the units of Z_{2^n}
  Quasigroups and Related Systems 18 (2010) 1, 59--82
  with Danilo Gligoroski and Smile Markovski
  arXiv, journal
  


• On capability of finite abelian groups
  Archiv der Mathematik (2009) 1, 23--28.
  arXiv, journal, paper
  


• Encouraging the grand coalition in convex cooperative games
  Studia Universitatis Babeş-Bolyai Mathematica (2009) 1, 3--19.
  with Titu Andreescu.
  arXiv, journal, paper
  


• A pastiche on embeddings into simple groups (following P. E. Schupp)
  Limits of graphs in group theory and computer science EPFL Press, 2009, 183--189.
  arXiv, book
  


• Groups generated by 3-state automata over a 2-letter alphabet, II
  Journal of Mathematical Sciences (NY) (2009) 1, 187--208.
  with I. Bondarenko, R. Grigorchuk, R. Kravchenko, Y. Muntyan, V. Nekrashevych, D. Savchuk
  arXiv, journal, paper
  


• Classification of groups generated by 3-state automata over a 2-letter alphabet
  Algebra and Discrete Mathematics (2008) 1, 1--163.
  with I. Bondarenko, R. Grigorchuk, R. Kravchenko, Y. Muntyan. V. Nekrashevych, D. Savchuk
  arXiv, journal, paper
  


• Schreier spectrum of the Hanoi Towers group on three pegs
  Proceedings of Symposia in Pure Mathematics 77 (2008), 183--198.
  with R. Grigorchuk.
  arXiv, series, volume
  


• Frobenius Problem and dead ends in integers
  Journal of Number Theory 128 (2008), no.5, 1211--1223.
  arXiv, journal, paper
  


• Rational tree morphisms and transducer integer sequences: definition and examples
  Journal of Integer Sequences, (2007) 4, Article 07.4.3 26pp.
  arXiv, journal, paper
  


• Groups generated by 3-state automata over a 2-letter alphabet, I
  São Paulo Journal of Mathematical Sciences (2007), no.1, 1--40.
  with I. Bondarenko, R. Grigorchuk, R. Kravchenko, Y. Muntyan. V., Nekrashevych, D. Savchuk
  arXiv, journal
  


• Hausdorff dimension in a family of self-similar groups
  Geometriae Dedicata 124 (2007), 213--236.
  arXiv, journal, paper


• Construction of elements in the closure of Grigorchuk group
  in The true prosoluble completion of a group: examples and open problems by Goulnara Arzhantseva, Pierre de la Harpe, Delaram Kahrobaei.
  Geometriae Dedicata (2007), 5--26.
  with Goulnara Arzhantseva.
  arXiv, journal, paper


• Self-similarity and branching in group theory
  London Mathematical Society Lecture Note Series 339 (2007), 36--95.
  with Rostislav Grigorchuk.
  pdf, series, volume


• Poly-free constructions for right-angled Artin groups
  Journal of Group Theory 10 (2007) 1, 117--138.
  with Susan Hermiller.
  arXiv, journal, paper


• Tamari lattices, forests, and Thompson monoids
  European Journal of Combinatorics 28 (2007) 4, 1216--1238.
  arXiv, journal, paper


• Bandwidth reduction in rectangular grids
  Algebra and Discrete Mathematics (2007) 2, 1--15.
  with Titu Andreescu and Walter Stromquist.
  journal, paper
  


• Asymptotic aspects of Schreier graphs and Hanoi Towers groups
  Comptes Rendus Mathématique, Académie des Sciences Pari 342 (2006) 8, 545--550.
  with Rostislav Grigorchuk.
  arXiv, journal, paper


• The spectral problem, substitutions and iterated monodromy
  CRM Proceedings and Lecture Notes 42 (2007), 225--248.
  with Rostislav Grigorchuk and Dmytro Savchuk.
  arXiv, series, volume
  


• Some solvable automaton groups
  Contemporary Mathematics 394 (2006), 11--29.
  with Laurent Bartholdi.
  arXiv, series, volume
  


• Distortion functions and the membership problem for submonoids of groups and monoids
  Contemporary Mathematics (2005), 109--129.
  with S. Margolis and J. Meakin.
  pdf, series, voume
  


• Self-describing sequences and the Catalan family tree
  The Electronic J. of Combinatorics (2003) 1, #N5, 9pp.
  arXiv, journal, paper
  


• Branch groups
  Handbook of Algebra, III, North-Holland, Amsterdam, 2003, 989--1112.
  with Laurent Bartholdi and Rostislav Grigorchuk.
  arXiv, book
  


• Young tableaux and other mutually describing sequences
  Journal of Integer Sequences (2002) 1, Article 02.1.5, 7pp.
  journal, paper
  


• On the word and period growth of some groups of tree automorphisms
  Communications in Algebra (2001) 11, 4923--4964.
  with Laurent Bartholdi.
  pdf, journal, paper

Announcements/Abstracts

• Hanoi Towers groups
  Oberwolfach Report 19/2006, 11--14.
  with Rostislav Grigorchuk and Volodymyr Nekrashevych.
  pdf
  


• Hanoi Towers group on 3 pegs and its pro-finite closure
  Oberwolfach Report 25/2006, 15--17.
  with Rostislav Grigorchuk and Volodymyr Nekrashevych.
  pdf
  

Undergraduate Exposition

• The birth of Combinalysis
  pdf
  


• An ideal functional equation with a ring
  Mathematics Magazine 77 (2004) 4, 310--313.
  journal, pdf
  


• Matrix inversion and the great injustice
  The College Mathematics Journal 33 (2002) 5
  journal, pdf
  


• Several Solutions to a Balkan Olympiad Problem
  Mathematics and Informatics Quarterly 7 (1997) 1, 15--19.
  journal

Colaborators

Titu Andreescu U of Texas at Dallas
Goulnara Arzhantseva U of Wien
Laurent Bartholdi U of Göttingen
Ievgen Bondarenko National U of Kyiv
Martin Bridson U of Oxford
José Burillo Politècnica Catalunya
T. Ceccherini-Silberstein Benevento
Murray Elder U of Newcastle
Francesca Fiorenzi Paris-Sud 11
Danilo Gligoroski NTNU Trondheim
Rostislav Grigorchuk Texas A&M
Susan Hermiller U of Nebraska
Rostyslav Kravchenko Texas A&M
Stuart Margolis Bar Ilan U
Smile Markovski Cyril & Methodius U
John Meakin U of Nebraska
Ievgen Muntyan, Microsoft Corporation
Volodymyr Nekrashevych Texas A&M
Dmytro Savchuk SUNY - Binghamton
Walter Stromquist Swarthmore C
Enric Ventura Politècnica Catalunya