Publications

Research:

• On capability of finite abelian groups,
  Archiv der Mathematik 93 (2009) 1, 23--28.
  (arXiv, access)
  
  
• 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, free access)
  
  
• Encouraging the grand coalition in convex cooperative games,
  Studia Universitatis Babeş-Bolyai Mathematica 54 (2009) 1, 3--19.
  with Titu Andreescu.
  (arXiv, access)
  
  
• A pastiche on embeddings into simple groups (following P. E. Schupp),
  in "Limits of graphs in group theory and computer science", EPFL Press, 2009, 183--189. 
  (arXiv, access)
  
  
• Schreier spectrum of the Hanoi Towers group on three pegs, 
  Proceedings of Symposia in Pure Mathematics 77 (2008), 183--198.
  with R. Grigorchuk.
  (arXiv, access)
  
  
• Groups generated by 3-state automata over a 2-letter alphabet, II,
  Journal of Mathematical Sciences (NY) 156 (2009) 1, 187--208.
  with I. Bondarenko, R. Grigorchuk, R. Kravchenko, Y. Muntyan. V. Nekrashevych, D. Savchuk
  (arXiv, access)
  
  
• Frobenius Problem and dead ends in integers,
  Journal of Number Theory 128 (2008), no.5, 1211--1223.
  (arXiv, access)
  
  
• Rational tree morphisms and transducer integer sequences: definition and examples,
  Journal of Integer Sequences 10 (2007) 4, Article 07.4.3 26pp.
  (free access) 
  
  
• Groups generated by 3-state automata over a 2-letter alphabet, I,
  São Paulo Journal of Mathematical Sciences 1 (2007),  no.1, 1--40.
  with I. Bondarenko, R. Grigorchuk, R. Kravchenko, Y. Muntyan, V. Nekrashevych, D. Savchuk.
  (arXiv)
  
  
• Hausdorff dimension in a family of self-similar groups,
  Geometriae Dedicata 124 (2007), 213--236. 
  (arXiv, access)
  
  
• Construction of  elements in the closure of Grigorchuk group,
  appendix to The true prosoluble completion of a group: examples and open problems by Goulnara Arzhantseva, Pierre de la Harpe, Delaram Kahrobaei,
  Geometriae Dedicata 124 (2007), 5--26.
  with Goulnara Arzhantseva.
  (arXiv, access)
  
  
• The spectral problem, substitutions and iterated monodromy,
  CRM Proceedings and Lecture Notes 42 (2007), 225--248.
  with Rostislav Grigorchuk and Dmytro Savchuk.
  (arXiv, access)
  
  
• Self-similarity and branching in group theory,
  London Mathematical Society Lecture Note Series 339 (2007), 36--95.
  with Rostislav Grigorchuk.
  (pdf, access)
  
  
• Asymptotic aspects of Schreier graphs and Hanoi Towers groups,
  Comptes Rendus Mathématique, Académie des Sciences Paris 342 (2006) 8, 545--550.
  with Rostislav Grigorchuk.
  (arXiv, access)
  
  
• Tamari lattices, forests and Thompson monoids,
  European Journal of Combinatorics 28 (2007) 4, 1216--1238.
  (arXiv, access)
  
  
• Poly-free constructions for right-angled Artin groups,
  Journal of Group Theory 10 (2007) 1, 117--138.
  with Susan Hermiller.
  (arXiv, access)
  
  
• Some solvable automaton groups,
  Contemporary Mathematics 394 (2006), 11--29.
  with Laurent Bartholdi.
  (arXiv, access)
  
  
• Distortion functions and the membership problem for submonoids of groups and monoids,
  Contemporary Mathematics 372 (2005), 109--129.
  with S. Margolis and J. Meakin.
  (pdf, access)
  
  
• Bandwidth reduction in rectangular grids,
  Algebra and Discrete Mathematics (2007) 2, 1--15.
  with Titu Andreescu and Walter Stromquist.
  (free access)
  
  
• Self-describing sequences and the Catalan family tree,
  The Electronic J. of Combinatorics 10 (2003) 1, #N5, 9pp.
  (free access)
  
  
• Young tableaux and other mutually describing sequences,
  Journal of Integer Sequences  5 (2002) 1, Article 02.1.5, 7pp.
  (free access)
  
  
• Branch groups,
  Handbook of Algebra, III, North-Holland, Amsterdam, 2003, 989--1112.
  with Laurent Bartholdi and  Rostislav Grigorchuk.
  (pdf, arXiv, access)
  
  
• On the word and period growth of some groups of tree automorphisms,
  Communications in Algebra 29 (2001) 11, 4923--4964.
  with Laurent Bartholdi.
  (pdf, access)

Research Abstracts/Announcements:

• 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:

• Discover disc covers!,
  Mathematical Reflections 1 (2006) 1, A3, 6pp. (electronic, free access)

• The birth of Combinalysis, (pdf)
• An ideal functional equation with a ring,
  Mathematics Magazine 77 (2004) 4, 310--313. (pdf)
• Matrix  inversion and the great injustice,
  The College Mathematics Journal 33 (2002) 5 (pdf)
• Several Solutions to a Balkan Olympiad Problem,
  Mathematics and Informatics Quarterly 7 (1997) 1, 15--19. 

Coauthors

• Titu Andreescu, University of Texas at Dallas
• Goulnara Arzhantseva, University of Geneva
• Laurent Bartholdi, Georg-August University of Göttingen
• Ievgen Bondarenko, National Taras Shevchenko University of Kyiv
• Rostislav Grigorchuk, Texas A&M University
• Susan Hermiller, University of Nebraska
• Rostyslav Kravchenko, Texas A&M University
• Stuart Margolis, Bar Ilan University
• John Meakin, University of Nebraska
• Ievgen Muntyan, Texas A&M University
• Volodymyr Nekrashevych, Texas A&M University
• Dmytro Savchuk, Texas A&M University
• Walter Stromquist, Swarthmore College