Professor Anthony (Tony) GUTTMANN


School of Mathematics and Statistics

  • Room: 194
  • Building: Peter Hall Building
  • Campus: Parkville Campus

Research Interests

  • Mathematical Physics
  • Enumerative combinatorics
  • Statistical Mechanics
  • Exact solutions of lattice models
  • Critical Phenomena (phase transitions)

Research Groups

Recent Publications

  • A. Guttmann, EJ Janse van Rensburg, I. Jensen, S. Whittington. Polygons pulled from an adsorbing surface. Journal of Physics A: Mathematical and Theoretical, 51, 2018. doi: 10.1088/1751-8121/aaa3b9.

  • N. Beaton, A. Guttmann, AR Conway. On consecutive pattern-avoiding permutations of length 4, 5 and beyond. Discrete Mathematics and Theoretical Computer Science, 19, 2018.

  • A. Elvey Price, AJ Guttmann, A. Guttmann. Permutations sortable by two stacks in series. Advances in Applied Mathematics, 83, 81-96, 2017. doi: 10.1016/j.aam.2016.09.003.

  • Andrew Elvey Price, A. Guttmann. Permutations sortable by deques and by two stacks in parallel. European Journal of Combinatorics, 59, 71-95, 2017. doi: 10.1016/j.ejc.2016.08.002.

  • AJ Guttmann, A. Guttmann, I. Jensen, J-M Maillard, J Pantone. Is the full susceptibility of the square-lattice Ising model a differentially algebraic function?. Journal of Physics A: Mathematical and Theoretical, 49, 504002 (36pp), 2016. doi: 10.1088/1751-8113/49/50/504002.

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Extra Information

My research interests are in equilibrium statistical mechanics in general, and more particularly in discrete models of phase transitions. As these are often equivalent to a combinatorial problem, I am equally interested in the relevant combinatorics, and the connection between the two. Additionally, I am regularly looking for new ways to count the underlying graphs efficiently. This leads me into a study of algorithmic complexity.

Current Postgraduate Supervision

Name Thesis title

Past Postgraduate Supervision

Name Thesis title
Nicholas BEATON "Combinatorics of Lattice Paths and Polygons"
Debra BENNETT-WOOD "Numerical studies of Self-avoiding walks"
Yao-ban CHAN "Selected problems in lattice statistical mechanics"
Will JAMES "The enumeration of heaps and almost-convex polygons"
Robin LANGER "Symmetric functions and Macdonald polynomials"
Andrew RECHNITZER "Some problems in the counting of lattice animals, polyominoes, polygons and walks"
Jason WHYTE "Global a priori identifiability of biomolecular interaction models in flow-cell optical biosensor experiments"
Henry (Ling Heng) WONG "Topics on Lattice Models in Statistical Mechanics"

Past MSc Students

Name Project title

Recent Grant History

Year(s) Source Type Title
2014 - 2016 ARC Discovery Advanced algorithms for statistical mechanical models (080078)
2012 - 2014 ARC Discovery Critical behaviour of lattice models of spin systems
2010 - 2012 ARC Discovery Green functions, correlation functions and differential equations
2008 - 2009 ARC Linkage International Hecke algebras and hidden symmetries in quantum spin chains
2003 - 2010 ARC Centre Of Excellence ARC Centre of Excellence for Mathematics and Statistics of Complex Systems


Year Name Organisation
2006 Szekeres Medal Australian Mathematical Society
2005 Lyle Medal Australian Academy of Science
2004 B H Neumann Australian Mathematics Trust
2002 Fellow of The Australian Academy of Science Australian Academy of Science
2000 Centenary Medal Australian Government
1998 Hannan Medal Australian Academy of Science


  • Academic Board member
  • AMSI Advisory Board
  • MASCOS Director
  • University of Melbourne School Maths Competition


  • Strategic Planning Committee