Publications

Research:

• 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)
  
  
• Encouraging the grand coalition in convex cooperative games, 2007, 12pp. with Titu Andreescu. (arXiv)
  
  
• A pastiche on embeddings into simple groups (following P. E. Schupp), 2007, 5pp. (arXiv)
  
  
• Schreier spectrum of the Hanoi Towers group on three pegs, accepted in Proceedings of Symposia in Pure Mathematics, 2008, 16pp. with R. Grigorchuk. (arXiv)
  
  
• Groups generated by 3-state automata over a 2-letter alphabet, II, 2007, 28pp. with I. Bondarenko, R. Grigorchuk, R. Kravchenko, Y. Muntyan. V. Nekrashevych, D. Savchuk (arXiv)
  
  
• 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, accepted in São Paulo Journal of Mathematical Sciences, 2006, 37pp. 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.