## 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

Link | PDF file | Show/Hide Abstract

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

Link | PDF file | Show/Hide Abstract

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+

Link | PDF file | Show/Hide Abstract

### PhD Thesis

*Combinatorics of Lattice Paths and Polygons*

Department of Mathematics and Statistics

The University of Melbourne, 2012

Link | PDF file | Show/Hide Abstract

© 2021 Nicholas Beaton

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