Papers

Most of my papers can be found on my arXiv page. See also my Google Scholar page and my ORCID page.

Preprints

Nicholas R. Beaton
Walks obeying two-step rules on the square lattice: full, half and quarter planes
Submitted.
arXiv | Code | Show/Hide Abstract

Nicholas R. Beaton, Leo Li, Jonathon Liu, and Thomas Wong
Semi-flexible directed polymers in a strip with attractive walls
Submitted.
arXiv | Show/Hide Abstract

Nicholas R. Beaton, Aleksander L. Owczarek, and Ruijie Xu
Quarter-plane lattice paths with interacting boundaries: the Kreweras and reverse Kreweras models
To appear.
arXiv | Show/Hide Abstract | Mathematica files

Publications

Nicholas R. Beaton, Geoffrey R. Grimmett, and Mark Holmes
Alignment percolation
Mathematical Physics, Analysis and Geometry 24 (2021) #3.
Link | arXiv | Show/Hide Abstract

Nicholas R. Beaton and Aleksander L. Owczarek
Exact solutions of directed walk models of polymeric zipping with pulling in two and three dimensions
Physica A: Statistical Mechanics and its Applications 566 (2021) 125635.
Link | arXiv | Show/Hide Abstract

Nicholas R. Beaton, Anthony J. Guttmann, and Iwan Jensen
Two-dimensional interacting self-avoiding walks: new estimates for critical temperatures and exponents
Journal of Physics A: Mathematical and Theoretical 53 (2020) 165002.
Link | arXiv | Show/Hide Abstract

Nicholas R. Beaton, Aleksander L. Owczarek, and Ruijie Xu
Quarter-plane lattice paths with interacting boundaries: Kreweras and friends
Proceedings of the 31st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2019, Ljubljana, Slovenia)
Link | PDF file | Show/Hide Abstract | Mathematica file

Nicholas R. Beaton, Aleksander L. Owczarek, and Andrew Rechnitzer
Exact solution of some quarter plane walks with interacting boundaries
Electronic Journal of Combinatorics 26 (2019) P3.53.
Link | arXiv | Show/Hide Abstract

Nicholas R. Beaton, Mathilde Bouvel, Veronica Guerrini, and Simone Rinaldi
Slicings of parallelogram polyominoes: Catalan, Schröder, Baxter, and other sequences
Electronic Journal of Combinatorics 26 (2019) P3.13.
Link | arXiv | Show/Hide Abstract

Nicholas R. Beaton, Mathilde Bouvel, Veronica Guerrini, and Simone Rinaldi
Enumerating five families of pattern-avoiding inversion sequences; and introducing the powered Catalan numbers
Theoretical Computer Science 777 (2019) 69-92.
Link | arXiv | Show/Hide Abstract

Nicholas R. Beaton, Jeremy W. Eng, and Christine E. Soteros
Knotting statistics for polygons in lattice tubes
Journal of Physics A: Mathematical and Theoretical 52 (2019) 144003.
Link | arXiv | PDF File | Show/Hide Abstract

Alireza Montazeri, Nicholas R. Beaton, and Dwight Makaroff
LRU-2 vs. 2-LRU: An Analytical Study
Proceedings of the IEEE 43rd Conference on Local Computer Networks (LCN), 2018.
Link | PDF file | Show/Hide Abstract | Copyright Notice

Nicholas R. Beaton, Jeremy W. Eng, Kai Ishihara, Koya Shimokawa, and Christine E. Soteros
Characterising knotting properties of polymers in nanochannels
Soft Matter 14 (2018), 5775-5785
Link | arXiv | PDF file and Electronic Supplementary Information | Show/Hide Abstract

Nicholas R. Beaton, Andrew R. Conway, and Anthony J. Guttmann
On consecutive pattern-avoiding permutations of length 4, 5 and beyond
Discrete Mathematics and Theoretical Computer Science 19 -- Special Issue for Permutation Patterns 2016 (2018), Article #8
Link | arXiv | PDF file | Show/Hide Abstract

Nicholas R. Beaton and E.J. Janse van Rensburg
Partition function zeros of adsorbing Dyck paths
Journal of Physics A: Mathematical and Theoretical 51 (2018), 114002
Link | arXiv | PDF file | Show/Hide Abstract

Nicholas R. Beaton
Adsorbing staircase polygons subject to a force
Journal of Physics A: Mathematical and Theoretical 50 (2017), 494001
Link | arXiv | PDF file | Show/Hide Abstract

Nicholas R. Beaton, Jeremy W. Eng, and Christine E. Soteros
Polygons in restricted geometries subjected to infinite forces
Journal of Physics A: Mathematical and Theoretical 49 (2016), 424002
Link | arXiv | PDF file | Show/Hide Abstract

$\rightarrow$ See also the version which appeared in
Proceedings of the 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016, Vancouver, Canada), 119-130
Link | PDF file | Show/Hide Abstract

Nicholas R. Beaton, Anthony J. Guttmann, Iwan Jensen, and Gregory F. Lawler
Compressed self-avoiding walks, bridges and polygons
Journal of Physics A: Mathematical and Theoretical 48 (2015), 454001
Link | arXiv | PDF file | Show/Hide Abstract

Nicholas R. Beaton and Gerasim K. Iliev
Two-sided prudent walks: A solvable non-directed model of polymer adsorption
Journal of Statistical Mechanics: Theory and Experiment (2015), P09014
Link | arXiv | PDF file | Show/Hide Abstract

Nicholas R. Beaton
The critical pulling force for self-avoiding walks
Journal of Physics A: Mathematical and Theoretical 48 (2015), 16FT03
Link | arXiv | PDF file | Show/Hide Abstract

Axel Bacher and Nicholas R. Beaton
Weakly prudent self-avoiding bridges
Proceedings of the 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014, Chicago, USA), 827-838
Link | PDF file | Show/Hide Abstract

Nicholas R. Beaton, Mireille Bousquet-Mélou, Jan de Gier, Hugo Duminil-Copin, and Anthony J. Guttmann
The critical fugacity for surface adsorption of self-avoiding walks on the honeycomb lattice is $1+\sqrt{2}$
Communications in Mathematical Physics 326 (2014), 727-754
Link | arXiv | PDF file | Show/Hide Abstract

Nicholas R. Beaton
The critical surface fugacity for self-avoiding walks on a rotated honeycomb lattice
Journal of Physics A: Mathematical and Theoretical 47 (2014), 075003+
Link | arXiv | PDF file | Show/Hide Abstract

$\rightarrow$ See also the version which appeared in
Proceedings of the 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013, Paris, France), 665-676
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Nicholas R. Beaton, Anthony J. Guttmann, and Iwan Jensen
Two-dimensional self-avoiding walks and polymer adsorption: Critical fugacity estimates
Journal of Physics A: Mathematical and Theoretical 45 (2012), 055208+
Link | arXiv | PDF file | Show/Hide Abstract

Nicholas R. Beaton, Anthony J. Guttmann, and Iwan Jensen
A numerical adaptation of SAW identities from the honeycomb to other 2D lattices
Journal of Physics A: Mathematical and Theoretical 45 (2012), 035201+
Link | arXiv | PDF file | Show/Hide Abstract

Nicholas R. Beaton, Philippe Flajolet, Timothy M. Garoni, and Anthony J. Guttmann
Some new self-avoiding walk and polygon models
Fundamenta Informaticae 117 (2012), 19-33
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Nicholas R. Beaton, Philippe Flajolet, and Anthony J. Guttmann
The enumeration of prudent polygons by area and its unusual asymptotics
Journal of Combinatorial Theory, Series A 118 (2011), 2261-2290
Link | arXiv | PDF file | Show/Hide Abstract

Nicholas R. Beaton, Filippo Disanto, Anthony J. Guttmann, and Simone Rinaldi
On the enumeration of column-convex permutominoes
Proceedings of the 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011, Reykjavik, Iceland), 111-122
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Nicholas R. Beaton, Philippe Flajolet, and Anthony J. Guttmann
The unusual asymptotics of three-sided prudent polygons
Journal of Physics A: Mathematical and Theoretical 43 (2010), 342001+
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PhD Thesis

Combinatorics of Lattice Paths and Polygons
Department of Mathematics and Statistics
The University of Melbourne, 2012
Link | PDF file | Show/Hide Abstract

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