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Publications

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Papers

1. S. Mertens
   Domination Polynomials of the Grid, the Cylinder, the Torus, and the King Graph
   Journal of Integer Sequences 27 Article 24.7.6 (2024)
2. C. Moore and S. Mertens
   Domination by kings is oddly even
   arXiv:2407.19344
3. S. Mertens
   Domination Polynomial of the Rook Graph
   Journal of Integer Sequences 27 Article 24.3.7 (2024)
4. J. L. Jacobsen, S. Mertens and C. R. Scullard
   A Biography of Robert M. Ziff
   J. Phys. A: Math. Theor. 56 410201 (2023)
5. S. Mertens
   Exact Site Percolation Probability on the Square Lattice
   J. Phys. A: Math. Theor. 55 334002 (2022)
6. S. Mertens and C. Moore
   Percolation is Odd
   Physical Review Letters 123 230605 (2019)
7. S. Mertens and C. Moore
   Percolation thresholds and Fisher exponents in hypercubic lattices
   Physical Review E 98 022120 (2018)
8. S. Mertens and C. Moore
   Series expansion of the percolation threshold on hypercubic lattices
   Journal of Physics A 51 475001 (2018)
9. S. Mertens, I. Jensen and R. M. Ziff
   Universal features of cluster numbers in percolation
   Physical Review E 96 052119 (2017)
10. S. Mertens and C. Moore
    Percolation Thresholds in Hyperbolic Lattices
    Physical Review E 96 042116 (2017)
11. S. Luther and S. Mertens
    The Perimeter of Proper Polycubes
    Journal of Integer Sequences 20 Article 17.9.5 (2017)
12. S. Mertens and R.M. Ziff
    Percolation in Finite Matching Lattices
    Physical Review E 94 062152 (2016)
13. T. Packebusch and S. Mertens
    Low Autocorrelation Binary Sequences
    Journal of Physics A 49 165001 (2016)
14. S. Mertens
    Small Random Instances of the Stable Roommates Problem
    Journal of Statistical Mechanics P06034 (2015)
15. S. Mertens
    Stable Roommates Problem with Random Preferences
    Journal of Statistical Mechanics P01020 (2015)
16. S. Mertens
    Viewpoint: A New Approach to the Matching Problem
    Physics 7 77 (2014)
17. S. Mertens and C. Moore
    The complexity of the fermionant, and immanants of constant width
    Theory of Computing 9 273 (2013)
18. S. Mertens and C. Moore
    Continuum Percolation Thresholds in Two Dimensions
    Physical Review E 86 061109 (2012)
19. S. Luther and S. Mertens
    Counting Lattice Animals in High Dimensions
    Journal of Statistical Mechanics P09026 (2011)
20. J. Machta, S. DeDeo, S. Mertens and C. Moore
    Parallel Complexity of Random Boolean Circuits
    Journal of Statistical Mechanics P04015 (2011)
21. S. Mertens and S. Boettcher
    Asymptotics of Lagged Fibonacci Sequences
    http://arXiv.org/abs/0912.2459
22. S. Mertens
    Random Number Generators: A Survival Guide for Large Scale Simulations
    Modern Computational Science 09, R. Leidl and A.K. Hartmann (eds), BIS-Verlag, Oldenburg, 2009
23. C. Borgs, J. Chayes, S. Mertens and C. Nair
    Proof of the local REM conjecture for number partitioning I: Constant energy scales
    Random Structures and Algorithms 34 217 (2008)
24. C. Borgs, J. Chayes, S. Mertens and C. Nair
    Proof of the local REM conjecture for number partitioning II: Growing energy scales
    Random Structures and Algorithms 34 241 (2008)
25. S. Mertens and S. Mingramm
    Brachistochrones with loose ends
    European Journal of Physics 29 1191 (2008)
26. S. Boettcher and S. Mertens
    Analysis of the Karmarkar-Karp Differencing Algorithm
    European Physics Journal B 65 131 (2008)
    arXiv.org:08024040
27. H. Bauke and S. Mertens
    Random Numbers for Large Scale Distributed Monte Carlo Simulations
    Physical Review E 75 066701 (2007)
    arxiv.org/abs/cond-mat/0609584
28. S. Mertens, M. Mézard and R. Zecchina
    Threshold values of random K-SAT from the cavity method
    Random Structures and Algorithms 28 340-373 (2006)
    arXiv.org/abs/cs.CC/0309020
29. S. Mertens
    Complexity Theory
    Lectures in Quantum Information, D. Bruss and G. Leuchs (eds), 125-139, Wiley VCH (2006)
30. S. Mertens
    The Easiest Hard Problem: Number Partitioning (Review)
    A.G. Percus, G. Istrate and C. Moore, eds., Computational Complexity and Statistical Physics (Oxford University Press, New York, 2006), p. 125-139
    arxiv.org/abs/cond-mat/0310317
31. S. Mertens
    Random Stable Matchings
    Journal of Statistical Mechanics (2005) P10008
    arxiv.org/abs/cond-mat/0509221
    see the Open Problem Garden
32. H. Bauke and S. Mertens
    Pseudo Random Coins Show More Heads Than Tails
    Journal of Statistical Physics 114 1149-1169 (2004)
    http://arxiv.org/abs/cond-mat/0307138
    see also the press coverage of this and the following paper
33. S. Mertens and H. Bauke
    Entropy of Pseudo Random Number Generators
    Physical Review E 69 055702(R) (2004)
    arxiv.org/abs/cond-mat/0305319
34. C. Borgs, J.T. Chayes, S. Mertens and B. Pittel
    Constrained Integer Partitions
    Proc. LATIN 2004 59--68, Springer Lecture Notes in Computer Science, vol. 2976 (2004),
35. H. Bauke, S. Franz and S. Mertens
    Number partitioning as random energy model
    Journal of Statistical Mechanics 2004 P04003 (2004)
    
36. H. Bauke and S. Mertens
    Universality in the level statistics of disordered systems
    Physical Review E 70 025102(R) (2004)
37. C. Borgs, J.T. Chayes, S. Mertens and B. Pittel
    Phase Diagram for the Constrained Integer Partitioning Problem
    Random Structures and Algorithms 24 315-380 (2004)
    arxiv.org/abs/cond-mat/0302536
38. H. Bauke, S. Mertens and A. Engel
    Phase Transition in Multiprocessor Scheduling
    Physical Review Letters 90 158701 (2003)
    see also Physics tackles processor problem by Kim Patch
    Technology Research News, November 19, 2003
39. S. Mertens
    Computational complexity for physicists (Review)
    Computing in Science & Engineering, vol.4, no.3, May/June 2002, pp. 31-47
40. S. Mertens
    A physicist’s approach to number partitioning
    Theoretical Computer Science 265 79-108 (2001)
    see also The Easiest Hard Problem by Brian Hayes
    American Scientist, March-April 2002
    also cited in Eric Weisstein’s mathworld
41. S. Mertens
    Random Costs in Combinatorial Optimization
    Physical Review Letters 84 1347 (2000)
42. S. Mertens
    A complete anytime algorithm for balanced number partitioning
    arXiv.org/abs/cs.DS/9903011
43. S. Mertens
    Phase transition in the number partitioning problem
    Physical Review Letters 81 4281 (1998)
44. S. Mertens and C. Bessenrodt
    On the ground states of the Bernasconi model
    Journal of Physics A 31 3731 (1998)
45. S. Mertens and A. Engel
    On the VC-dimension of neural networks with binary weights
    Physical Review E55 4478 (1997)
46. S. Mertens
    Exhaustive Search for Low Autocorrelation Binary Sequences
    Journal of Physics A 29 L473 (1996)
47. S. Mertens
    On the Vapnik-Chervonenkis Dimension of the Ising-Perceptron
    Journal of Physics 29 L199 (1996)
48. S. Mertens and M.E. Lautenbacher
    Counting Lattice Animals: A Parallel Attack
    Journal of Statistical Physics 66 669 (1992)
49. S. Mertens
    Lattice Animals: A Fast Enumeration Algorithm and New Perimeter Polynomials
    Journal of Statistical Physics 58 1095 (1990)
    also cited in Eric Weisstein’s mathworld
50. S. Mertens, H.M. Köhler and S. Bös
    Learning grey-toned patterns in neural networks
    Journal of Physics A 24 4941 (1991)
51. S. Mertens
    An extremely diluted asymmetric network with graded response neurons
    Journal of Physics 24 337 (1991)
52. E. Gardner, S. Mertens and A. Zippelius
    Retrieval properties of a neural network with an asymmetric learning rule
    Journal of Physics 22 2009 (1989)

Books

• C. Moore and S. Mertens
  The Nature of Computation
  Oxford University Press (2011)
  www.nature-of-computation.org
• H. Bauke and S. Mertens
  Cluster Computing
  Springer-Verlag, Berlin, Heidelberg, New York (2005)
  www.clustercomputing.de

Book Reviews

• On the Back of an Envelope
  A review of Guesstimation. Solving the World's Problems on the Back of a Cocktail Napkin
  by Lawrence Weinstein and John A. Adam, 319 pp., Princeton University Press, Princeton, NJ, 2008
  Science 321 1160, (2008)
• Connecting the Dots
  A review of Nets, Puzzles and Postmen. An exploration of mathematical connections.
  by Peter M. Higgins, 255 pp., Oxford University Press, 2007
  Science 320 181, (2008)
• The Revolution Will Be Digitized
  A review of Phase Change. The Computer Revolution in Science and Mathematics
  by Douglas S. Robertson, xi + 190 pp., Oxford University Press, 2003
  American Scientist 92, March-April (2004)
• Node by Node
  A review of Linked: The New Science of Networks
  by Albert-László Barabási, viii + 280 pp., Perseus Publishing, 2002
  American Scientist 91, March-April (2003)