World's Best Scientists 2026 revealed!
Anthony J. Guttmann

Anthony J. Guttmann

D-Index & Metrics

Mathematics

D-Index
54
Citations
8027
World Ranking
862
National Ranking
20

Anthony J. Guttmann publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where Anthony J. Guttmann sits on this spectrum.

42–46 publications: 3 scientists 47–51 publications: 5 scientists 52–56 publications: 7 scientists 57–61 publications: 20 scientists 62–66 publications: 14 scientists 67–71 publications: 25 scientists 72–76 publications: 19 scientists 77–81 publications: 35 scientists 82–86 publications: 50 scientists 87–91 publications: 60 scientists 92–96 publications: 86 scientists 97–101 publications: 84 scientists 102–106 publications: 83 scientists 107–111 publications: 90 scientists 112–116 publications: 99 scientists 117–121 publications: 90 scientists 122–126 publications: 91 scientists 127–131 publications: 109 scientists 132–136 publications: 110 scientists 137–141 publications: 98 scientists 142–146 publications: 112 scientists 147–151 publications: 102 scientists 152–156 publications: 88 scientists 157–161 publications: 106 scientists 162–166 publications: 83 scientists 167–171 publications: 102 scientists 172–176 publications: 77 scientists 177–181 publications: 81 scientists 182–186 publications: 78 scientists 187–191 publications: 71 scientists 192–196 publications: 92 scientists 197–201 publications: 64 scientists 202–206 publications: 69 scientists 207–211 publications: 64 scientists 212–216 publications: 62 scientists 217–221 publications: 58 scientists 222–226 publications: 53 scientists 227–231 publications: 50 scientists 232–236 publications: 46 scientists 237–241 publications: 46 scientists 242–246 publications: 46 scientists 247–251 publications: 43 scientists 252–256 publications: 29 scientists 257–261 publications: 45 scientists 262–266 publications: 30 scientists 267–271 publications: 33 scientists 272–276 publications: 34 scientists 277–281 publications: 30 scientists 282–286 publications: 31 scientists 287–291 publications: 21 scientists 292–296 publications: 34 scientists 297–301 publications: 26 scientists 302–306 publications: 10 scientists 307–311 publications: 17 scientists 312–316 publications: 23 scientists 317–321 publications: 13 scientists 322–326 publications: 16 scientists 327–331 publications: 26 scientists 332–336 publications: 13 scientists 337–341 publications: 13 scientists 342–346 publications: 16 scientists 347–351 publications: 17 scientists 352–356 publications: 12 scientists 357–361 publications: 18 scientists 362–366 publications: 18 scientists 367–371 publications: 9 scientists 372–376 publications: 11 scientists 377–381 publications: 8 scientists 382–386 publications: 8 scientists 387–391 publications: 9 scientists 392–396 publications: 9 scientists 397–401 publications: 8 scientists 402–406 publications: 11 scientists 407–411 publications: 6 scientists 412–416 publications: 6 scientists 417–421 publications: 9 scientists 422–426 publications: 8 scientists 427–431 publications: 5 scientists 432–436 publications: 8 scientists 437–441 publications: 8 scientists 442–446 publications: 4 scientists 447–451 publications: 4 scientists 452–456 publications: 4 scientists 457–461 publications: 2 scientists 462–466 publications: 2 scientists 467–471 publications: 4 scientists 472–476 publications: 3 scientists 477–481 publications: 3 scientists 482–486 publications: 6 scientists 487–491 publications: 3 scientists 492–496 publications: 5 scientists 497–501 publications: 5 scientists 502–506 publications: 1 scientists 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientists 522–526 publications: 3 scientists 527–531 publications: 1 scientists 532–536 publications: 4 scientists 537+ publications: 100 scientists
42 publications 537+

This scientist: 281 publications — 83rd percentile

83% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

Anthony J. Guttmann D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where Anthony J. Guttmann sits on this spectrum.

30 D-Index: 174 scientists 31 D-Index: 151 scientists 32 D-Index: 174 scientists 33 D-Index: 117 scientists 34 D-Index: 136 scientists 35 D-Index: 127 scientists 36 D-Index: 145 scientists 37 D-Index: 153 scientists 38 D-Index: 150 scientists 39 D-Index: 150 scientists 40 D-Index: 138 scientists 41 D-Index: 136 scientists 42 D-Index: 93 scientists 43 D-Index: 108 scientists 44 D-Index: 115 scientists 45 D-Index: 112 scientists 46 D-Index: 103 scientists 47 D-Index: 75 scientists 48 D-Index: 59 scientists 49 D-Index: 67 scientists 50 D-Index: 60 scientists 51 D-Index: 57 scientists 52 D-Index: 59 scientists 53 D-Index: 62 scientists 54 D-Index: 60 scientists 55 D-Index: 50 scientists 56 D-Index: 42 scientists 57 D-Index: 54 scientists 58 D-Index: 50 scientists 59 D-Index: 42 scientists 60 D-Index: 41 scientists 61 D-Index: 35 scientists 62 D-Index: 40 scientists 63 D-Index: 21 scientists 64 D-Index: 31 scientists 65 D-Index: 27 scientists 66 D-Index: 29 scientists 67 D-Index: 19 scientists 68 D-Index: 25 scientists 69 D-Index: 17 scientists 70 D-Index: 18 scientists 71 D-Index: 12 scientists 72 D-Index: 14 scientists 73 D-Index: 13 scientists 74 D-Index: 18 scientists 75 D-Index: 9 scientists 76 D-Index: 11 scientists 77 D-Index: 10 scientists 78 D-Index: 9 scientists 79 D-Index: 16 scientists 80 D-Index: 12 scientists 81 D-Index: 10 scientists 82 D-Index: 5 scientists 83 D-Index: 5 scientists 84 D-Index: 13 scientists 85 D-Index: 6 scientists 86+ D-Index: 99 scientists
30 D-Index 86+

This scientist: 54 D-Index — 78th percentile

78% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

Research.com Recognitions

  • 2009 - SIAM Fellow For contributions to statistical mechanics, combinatorics and their connections.

Overview

Anthony J. Guttmann is affiliated with the University of Melbourne in Australia and has contributed extensively to research in mathematics and computer science. Their work spans multiple subfields including discrete mathematics and combinatorics, computational theory and mathematics, mathematical physics, artificial intelligence, and statistics and probability.

The scientist's research topics cover advanced combinatorial mathematics, semigroups and automata theory, stochastic processes and statistical mechanics, Bayesian methods and mixture models, cellular automata and applications, random matrices and applications, and digital image processing techniques.

Recent publications by Anthony J. Guttmann include:

  • Self-avoiding walks contained within a square, 2022, Journal of Physics A Mathematical and Theoretical
  • Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices, 2022, Journal of Physics A Mathematical and Theoretical
  • On the existence of critical exponents for self-avoiding walks, 2022, Journal of Physics A Mathematical and Theoretical
  • Stieltjes Moment Sequences for Pattern-Avoiding Permutations, 2020, The Electronic Journal of Combinatorics
  • Pattern-Avoiding Ascent Sequences of Length 3, 2022, The Electronic Journal of Combinatorics

Frequent coauthors collaborating with Anthony J. Guttmann are:

  • Iwan Jensen
  • Andrew Conway
  • Andrew Elvey Price
  • J.-M. Maillard

Their scholarly output has been published in various venues, with the most frequent including:

  • arXiv (Cornell University)
  • The Electronic Journal of Combinatorics
  • Journal of Physics A Mathematical and Theoretical
  • RAIRO. Theoretical informatics and applications
  • Advances in Applied Mathematics

Anthony J. Guttmann has been recognized as a SIAM Fellow since 2009 for contributions related to statistical mechanics, combinatorics, and their connections.

Best Publications

  • Vicious walkers, friendly walkers and Young tableaux: II. With a wall

    Christian Krattenthaler;Anthony J Guttmann;Xavier G Viennot

  • On two-dimensional directed percolation

    J W Essam;A J Guttmann;K De'Bell

  • On the critical behaviour of self-avoiding walks

    A J Guttmann

  • Polygons, Polyominoes and Polycubes

    Anthony J. Guttmann

  • Algebraic techniques for enumerating self-avoiding walks on the square lattice

    A R Conway;I G Enting;A J Guttmann

  • Lattice Green functions in all dimensions

    Anthony J Guttmann

  • Square Lattice Self-Avoiding Walks and Corrections to Scaling.

    A. R. Conway;A. J. Guttmann

  • The Susceptibility of the Square Lattice Ising Model: New Developments

    W. P. Orrick;B. Nickel;A. J. Guttmann;J. H. H. Perk

  • Vicious walkers and Young tableaux I: without walls

    Anthony J Guttmann;Aleksander L Owczarek;Xavier G Viennot

  • The asymptotic behaviour of selfavoiding walks and returns on a lattice

    M F Sykes;A J Guttmann;M G Watts;P D Roberts

  • Some tests of scaling theory for a self-avoiding walk attached to a surface

    M N Barber;A J Guttmann;K M Middlemiss;G M Torrie

  • On a new method of series analysis in lattice statistics

    A J Guttmann;G S Joyce

  • Lattice Green's functions in all dimensions

    Anthony J Guttmann

  • Solvability of Some Statistical Mechanical Systems

    AJ Guttmann;IG Enting

  • Self-avoiding polygons on the square lattice

    Iwan Jensen;Anthony J Guttmann

  • The size and number of rings on the square lattice

    A J Guttmann;I G Enting

  • Exact solution of the staircase and row-convex polygon perimeter and area generating function

    R Brak;A J Guttmann

  • Statistics of lattice animals (polyominoes) and polygons

    Iwan Jensen;Anthony J Guttmann

  • A collapse transition in a directed walk model

    R Brak;A J Guttmann;S G Whittington

  • Vicious walkers and directed polymer networks in general dimensions.

    JW Essam;AJ Guttmann

  • Two-dimensional lattice vesicles and polygons

    M E Fisher;A J Guttmann;S G Whittington

Frequent Co-Authors

Iwan Jensen
Iwan Jensen Flinders University
Stuart G. Whittington
Stuart G. Whittington University of Toronto
Jesper Lykke Jacobsen
Jesper Lykke Jacobsen École Normale Supérieure
Mireille Bousquet-Mélou
Mireille Bousquet-Mélou University of Bordeaux
Jacques H. H. Perk
Jacques H. H. Perk Oklahoma State University
Philippe Flajolet
Philippe Flajolet French Institute for Research in Computer Science and Automation - INRIA
Christian Krattenthaler
Christian Krattenthaler University of Vienna
Barry W. Ninham
Barry W. Ninham Australian National University
Nicholas C. Wormald
Nicholas C. Wormald Monash University
John Cardy
John Cardy University of California, Berkeley

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