## Papers

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

### Preprints

Chris J. Bradly, Nicholas R. Beaton and Aleksander L. Owczarek

Lattice polymers near a permeable interface

arXiv | Show/Hide Abstract

Nicholas R. Beaton, Mark Holmes and Xin Huang

Chemical distance for the half-orthant model

arXiv | Show/Hide Abstract

Nicholas R. Beaton, Kai Ishihara, Mahshid Atapour, Jeremy W. Eng, Mariel Vazquez, Koya Shimokawa, and Christine E. Soteros

Entanglement statistics of polymers in a lattice tube and unknotting of 4-plats

arXiv | Show/Hide Abstract

### Publications

Nicholas R. Beaton, Kai Ishihara, Mahshid Atapour, Jeremy W. Eng, Mariel Vazquez, Koya Shimokawa, and Christine E. Soteros

A first proof of knot localization for polymers in a nanochannel

*Journal of Physics A: Mathematical and Theoretical* **57** (2024) 38LT01

Link | Show/Hide Abstract

Nicholas R. Beaton and Aleksander L. Owczarek

Exact solution of weighted partially directed walks crossing a square

*Journal of Physics A: Mathematical and Theoretical* **56** (2023) 155003

Link | arXiv | Show/Hide Abstract

Nicholas R. Beaton and Mark Holmes

The mean square displacement of random walk on the Manhattan lattice

*Statistics & Probability Letters* **193** (2023) 109706

Link | arXiv | Show/Hide Abstract

Nicholas R. Beaton

Walks obeying two-step rules on the square lattice: full, half and quarter planes

*Electronic Journal of Combinatorics* **29** (2022) P1.14

Link | arXiv | Code | 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

*Transcendence in Algebra, Combinatorics, Geometry and Number Theory (Proceedings of Trans'19)*

Springer Proceedings in Mathematics & Statistics, Volume 373 (2021), 163-192.

Link | arXiv | Show/Hide Abstract | Mathematica files

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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