## Papers

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

### Preprints

Ruijie Xu, Nicholas R. Beaton and Aleksander L. Owczarek

* Quarter-plane lattice paths with interacting boundaries: Kreweras and friends *

Submitted to FPSAC 2019.

PDF file | Show/Hide Abstract | Mathematica file

Nicholas R. Beaton, Mathilde Bouvel, Veronica Guerrini and Simone Rinaldi

* Enumerating five families of pattern-avoiding inversion sequences; and introducing the powered Catalan numbers*

arXiv | Show/Hide Abstract

Nicholas R. Beaton, Aleksander L. Owczarek and Andrew Rechnitzer

*Exact solution of some quarter plane walks with interacting boundaries*

arXiv | Show/Hide Abstract

Alireza Montazeri, Nicholas R. Beaton and Dwight Makaroff

*LRU-2 vs. 2-LRU: An Analytical Study*

To appear in the Proceedings of the IEEE 43rd Conference on Local Computer Networks (LCN), 2018

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Nicholas R. Beaton, Mathilde Bouvel, Veronica Guerrini and Simone Rinaldi

* Slicings of parallelogram polyominoes: Catalan, Schröder, Baxter, and other sequences*

arXiv | Show/Hide Abstract

### Publications

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 | 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

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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

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Nicholas R. Beaton

* Adsorbing staircase polygons subject to a force *

Journal of Physics A: Mathematical and Theoretical **50** (2017), 494001

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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

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$\rightarrow$ 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

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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

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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

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Nicholas R. Beaton

*The critical pulling force for self-avoiding walks*

Journal of Physics A: Mathematical and Theoretical **48** (2015), 16FT03

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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

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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

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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+

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$\rightarrow$ 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+

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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+

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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

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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

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© 2017 Nicholas Beaton

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