Textbooks

• See my textbooks and notes page.

Journal Articles

2026

A. Rechnitzer
The first 128 digits of an autoconvolution inequality
Preprint · arXiv

J. Cantarella, A. Rechnitzer, H. Schumacher, C. Shonkwiler
New upper bounds for stick numbers
Journal of Knot Theory and Its Ramifications, 2650008 (2026) · arXiv

M. Aggarwal, M. Elder, A. Rechnitzer
On groups with D-finite cogrowth series
Preprint · arXiv

2025

A.L. Owczarek, A. Rechnitzer
Exact solution of asymmetric gelation between three walks on the square lattice
J. Phys. A: Math. Theor. 58, 425001 (2025) · arXiv

2022

H. Chapman, A. Rechnitzer
A Markov chain sampler for plane curves
Experimental Mathematics 31, 552-582 (2022) · PDF · arXiv

2020

M.A. Bennett, G. Martin, K. O'Bryant, A. Rechnitzer
Counting Zeros of Dirichlet L-Functions
Math. Comp. 90, 1455-1482 (2021) · PDF · arXiv · Code/Data

2019

N.R. Beaton, A.L. Owczarek, A. Rechnitzer
Exact solution of some quarter plane walks with interacting boundaries
Electronic Journal of Combinatorics 26, P3.53 (2019) · PDF · arXiv

M.A. Bennett, A. Gherga, A. Rechnitzer
Computing elliptic curves over Q
Math. Comp. 88, 1341-1390 (2019) · PDF · Code/Data

2018

M.A. Bennett, G. Martin, K. O'Bryant, A. Rechnitzer
Explicit bounds for primes in arithmetic progressions
Illinois J. Math. Volume 62, Number 1-4, 427-532 (2018) · PDF · arXiv · Code/Data

M. Bouvel, V. Guerrini, A. Rechnitzer, S. Rinaldi
Semi-Baxter and strong-Baxter: two relatives of the Baxter sequence
SIAM J Discrete Math 32, pp. 2795-2819 (2018) · arXiv

Y-B. Chan, A. Rechnitzer
Upper bounds on the growth rates of hard squares and related models via corner transfer matrices
Linear Algebra and its Applications 555, pp 139-156 (2018) · PDF · arXiv

2017

A.L. Owczarek, A. Rechnitzer
Force signature of the unzipping transition for strip confined two-dimensional polymers
J. Phys. A: Math. Theor. 50, 484001 (2017) - selected for the journal's 'Highlights of 2017' collection · PDF

2016

R. Tabbara, A.L. Owczarek, A. Rechnitzer
An exact solution of three interacting friendly walks in the bulk
J. Phys. A: Math. Theor. 49, 154004 (2016) · arXiv

2015

M. Elder, A. Rechnitzer, E.J. Janse van Rensburg
Random sampling of trivial words in finitely presented groups
Experimental Mathematics 24, 391-409 (2015) · PDF · arXiv

M. Elder, G. Lee, A. Rechnitzer
Permutations generated by a depth 2 stack and an infinite stack in series are algebraic
Electronic Journal of Combinatorics 22, P2.16 (2015) · PDF · arXiv

2014

T. Wong, A.L. Owczarek, A. Rechnitzer
Confining multiple polymers between sticky walls: a directed walk model of two polymers
J. Phys. A: Math. Theor. 47: 415002 (2014) · PDF · arXiv

Y-B. Chan, A. Rechnitzer
Accurate lower bounds on two-dimensional constraint capacities from corner transfer matrices
IEEE Transactions on Information Theory 60: 3845-3858 (2014) · PDF · arXiv

M. Elder, A. Rechnitzer, E.J. Janse van Rensburg, T. Wong
The cogrowth series for BS(N,N) is D-finite
International Journal of Algebra and Computation 24: 171-187 (2014) · PDF · arXiv
Data: algebraic equations for G(z,q) for N=1..10 (pubs/data/alg_eqn.txt); differential equations for cogrowth series for N=1 (pubs/data/ode11.txt), N=2 (pubs/data/ode22.txt), N=3 (pubs/data/ode33.txt), N=4 (pubs/data/ode44.txt), N=5 (pubs/data/ode55.txt). -

R. Tabbara, A.L. Owczarek, A. Rechnitzer
An exact solution of two friendly interacting directed walks near a sticky wall
J. Phys. A: Math. Theor. 47: 015202 (2014) · PDF

2013

S. Cleary, A. Rechnitzer, T. Wong
Common edges in rooted trees and polygonal triangulations
Electronic Journal of Combinatorics 20: P39 (2013) · PDF

2012

M. Elder, A. Rechnitzer, T. Wong
On the cogrowth of Thompson's group F
Groups, Complexity, and Cryptology 4: 301-320 (2012) · PDF · arXiv

A.L. Owczarek, A. Rechnitzer, T. Wong
Exact solution of two friendly walks above a sticky wall with single and double interactions
J. Phys. A: Math. Theor. 45: 425003 (2012) · PDF · arXiv

Y-B. Chan, A. Rechnitzer
A Monte Carlo study of non-trapped self-avoiding walks
J. Phys. A: Math. Theor. 45: 405004 (2012) · PDF

D. Gasumova, E.J. Janse van Rensburg, A. Rechnitzer
Lattice knots in a slab
J. Stat. Mech. Theo. Expr. P09004 (2012) · PDF

E.J. Janse van Rensburg, A. Rechnitzer
The compressibility of minimal lattice knots
J Stat Mech: Theo Expr P05003 (2012) · PDF · arXiv

2011

E.J. Janse van Rensburg, A. Rechnitzer
Minimal knotted polygons in cubic lattices
Journal of Statistical Mechanics: Theory and Experiment: P09008 (2011) · PDF · arXiv

E.J. Janse van Rensburg, A. Rechnitzer
Generalised atmospheric sampling of knotted polygons
Journal of Knot Theory and Its Ramifications 20: 1145-1171 (2011) · PDF

E.J. Janse van Rensburg, A. Rechnitzer
On the universality of knot probability ratios
J. Phys. A: Math. Theor. Fast track communications, 44: 162002 (2011) · PDF · arXiv

E.J. Janse van Rensburg, A. Rechnitzer
BFACF-style algorithms for polygons in the body-centered and face-centered cubic lattices
J. Phys. A: Math. Theor. 44: 165001 (2011) · PDF · arXiv

2010

M. Elder, A. Rechnitzer
Some geodesic problems for finitely generated groups
Groups, Complexity, Cryptology 2: 223-229 (2010) · arXiv

M. Elder, É. Fusy, A. Rechnitzer
Counting elements and geodesics in Thompson's group F
Journal of Algebra 324: 102-121 (2010) · PDF · arXiv

S. Cleary, M. Elder, A. Rechnitzer, J. Taback
Random subgroups of Thompson's group F
Groups, Geometry and Dynamics 4: 91-126 (2010) · PDF · arXiv

2009

J. Alvarez, M. Gara, E.J. Janse van Rensburg, A. Rechnitzer
Atmospheric Collapse in Self-Avoiding Walks: A Numerical Study using GARM
Journal of Statistical Mechanics: Theory and Experiment: P12005 (2009) · PDF

E.J. Janse van Rensburg, A. Rechnitzer
Generalised atmospheric sampling of self-avoiding walks
J. Phys. A: Math. Theor. 42: 335001 (2009) · PDF

H. Lonsdale, R. Brak, J.W. Essam, A.L. Owczarek, A. Rechnitzer
On directed compact percolation near a damp wall
J. Phys. A: Math. Theor. 42: 125001 (2009) · PDF

M. Mishna, A. Rechnitzer
Two non-holonomic lattice walks in the quarter plane
Theoret. Comput. Sci. 410: 3616-3630 (2009) · PDF · arXiv

R. Brak, P. Dyke, J. Lee, A.L. Owczarek, T. Prellberg, A. Rechnitzer, S.G. Whittington
A self-interacting partially directed walk subject to a force
J. Phys. A: Math. Theor. 42: 085001 (2009) · PDF · arXiv

2008

A. Rechnitzer, E.J. Janse van Rensburg
Generalised Atmospheric Rosenbluth Methods (GARM)
Journal of Physics A: Mathematical and Theoretical (Fast Track Communications), 41: 442002 (2008) · PDF · arXiv

I. Jensen, A. Rechnitzer
Exact perimeter generating function for a model of punctured staircase polygons
Journal of Physics A: Mathematical and Theoretical, 41: 215002 (2008) · PDF

E.J. Janse van Rensburg, A. Rechnitzer
Atmospheres of polygons and knotted polygons
Journal of Physics A: Mathematical and Theoretical, 41: 105002 (2008) · PDF

A.L. Owczarek, T. Prellberg, A. Rechnitzer
Finite-size scaling functions for directed polymers confined between attracting walls
Journal of Physics A: Mathematical and Theoretical, 41: 035002 (2008) · PDF · arXiv

E.J. Janse van Rensburg, T. Prellberg, A. Rechnitzer
Partially directed paths in a wedge
J. Combinatorial Theory - Series A, 115: 623-650 (2008) · PDF · arXiv

2007

A.L. Owczarek, A. Rechnitzer, T. Prellberg, J. Krawczyk
On the location of the surface-attached globule phase in collapsing polymers
Journal of Physics A: Mathematical and Theoretical, 40: 13257-13267 (2007) · PDF · arXiv

E.J. Janse van Rensburg, T. Prellberg, A. Rechnitzer
Directed paths in a wedge
Journal of Physics A: Mathematical and Theoretical, 40: 14069-14084 (2007) · arXiv

J. Krawczyk, A.L. Owczarek, T. Prellberg, A. Rechnitzer
A lattice model for parallel and orthogonal beta-sheets using hydrogen-like bonding
Physical Review E: 76, 051904 (2007) · PDF · arXiv
Selected to appear in the Virtual Journal of Biological Physics Research.

R. Martin, E. Orlandini, A.L. Owczarek, A. Rechnitzer, S.G. Whittington
Exact enumeration and Monte Carlo results for self-avoiding walks in a slab
Journal of Physics A: Mathematical and Theoretical, 40: 7509-7521 (2007) · PDF

R. Brak, G.K. Iliev, A. Rechnitzer, S.G. Whittington
Motzkin path models of long chain polymers in slits
Journal of Physics A: Mathematical and Theoretical, 40: 4415-4437 (2007) · PDF

Y. Chan, A.L. Owczarek, A. Rechnitzer, G. Slade
Mean unknotting times of random knots and embeddings
Journal of Statistical Mechanics: Theory and Experiment, P05004 (2007) · PDF

2006

R. Brak, S. Corteel, J. Essam, R. Parviainen, A. Rechnitzer
A Combinatorial derivation of the PASEP stationary state
Electronic Journal of Combinatorics 13: R108 (2006) · PDF

J. Krawczyk, T. Prellberg, A.L. Owczarek, A. Rechnitzer
On a type of self-avoiding random walk with multiple site weightings and restrictions
Physical Review Letters 96: 240603 (2006) · PDF
Selected to appear in the Virtual Journal of Biological Physics Research.

R. Brak, J. Essam, J. Osborn, A.L. Owczarek, A. Rechnitzer
Lattice paths and the constant term
Journal of Physics: Conference Series, 42: 47-58 (2006) · PDF

A.L. Owczarek, A. Rechnitzer
On the number of anisospiral walks: a challenge in numerical analysis
Journal of Physics: Conference Series, 42: 225-230 (2006) · PDF

E.J. Janse van Rensburg, E. Orlandini, A.L. Owczarek, A. Rechnitzer, S.G. Whittington
Self-avoiding walks in a slab with attractive walls
J. Phys. A: Math. Gen., 38: L823-828 (2005) · PDF
Published 2005, appeared in 2006 issue.

M.H. Albert, M. Elder, A. Rechnitzer, P. Westcott, M. Zabrocki
On the Wilf-Stanley limit of 4231-avoiding permutations and a conjecture of Arratia
Advances in Applied Mathematics 36: 96-105 (2006) · PDF · arXiv

A. Rechnitzer
Haruspicy 3: The anisotropic generating function of directed bond-animals is not D-finite
J. Combinatorial Theory - Series A, 113: 1031-1049 (2006) · PDF · arXiv

A. Rechnitzer
Haruspicy 2: The anisotropic generating function of self-avoiding polygons is not D-finite
J. Combinatorial Theory - Series A, 113: 520-546 (2006) · PDF · arXiv

T. Prellberg, J. Krawczyk, A. Rechnitzer
Polymer simulations with a flat histogram stochastic growth algorithm
In Computer Simulation Studies in Condensed Matter Physics XVII, Springer Verlag (2006) · PDF · arXiv

2005

R. Brak, A.L. Owczarek, A. Rechnitzer, S.G. Whittington
A directed walk model of a long chain polymer in a slit with attractive walls
J. Phys. A: Math. Gen., 38: 4309-4325 (2005) · PDF

A.J. Guttmann, R. Parviainen, A. Rechnitzer
Self-avoiding walks and trails on the 3.12^2 lattice
J. Phys. A: Math. Gen., 38: 543-554 (2005) · PDF · arXiv

J. Krawczyk, T. Prellberg, A.L. Owczarek, A. Rechnitzer
Pulling adsorbing and collapsing polymers from a surface
J. Stat. Mech.: Theor. Exp. P05008 (2005) · PDF · arXiv

G. Iliev, A. Rechnitzer, S.G. Whittington
Localization of random copolymers and the Morita approximation
J. Phys. A: Math. Gen., 38: 1209-1223 (2005) · PDF

J. Krawczyk, T. Prellberg, A.L. Owczarek, A. Rechnitzer
Layering transitions for adsorbing polymers in poor solvents
Europhys. Lett., 70: 726-732 (2005) · PDF · arXiv

2004

J. Krawczyk, T. Prellberg, A. Rechnitzer, A.L. Owczarek
Stretching of a chain polymer adsorbed at a surface
J. Stat. Mech.: Theor. Exp. P10004 (2004) · PDF · arXiv

E.J. Janse van Rensburg, A. Rechnitzer
Multiple Markov chain Monte Carlo study of adsorbing self-avoiding walks in two and three dimensions
J. Phys. A: Math. Gen., 37: 6875-6898 (2004) · PDF

A. Rechnitzer, E.J. Janse van Rensburg
Exchange relations, Dyck paths and copolymer adsorption
Discrete Applied Mathematics 150: 49-71 (2004) · PDF

2003

E.J. Janse van Rensburg, A. Rechnitzer
High precision canonical Monte Carlo determination of the growth constant of square lattice trees
Physical Review E, 67: 036116 (2003) · PDF

A. Rechnitzer
Haruspicy and anisotropic generating functions
Advances in Applied Mathematics 30: 228-257 (2003) · PDF

M. Bousquet-Melou, A. Rechnitzer
The site-perimeter of bargraphs
Advances in Applied Mathematics 31: 86-112 (2003) · PDF

2002

E.J. Janse van Rensburg, A. Rechnitzer
Exchange symmetries in Motzkin paths and bargraph models of copolymer adsorption
Electronic Journal of Combinatorics 9 (2002) · PDF

A. Rechnitzer, E.J. Janse van Rensburg
Canonical Monte Carlo determination of the connective constant of self-avoiding walks
J. Phys. A; Math. Gen., 35: L605-L612 (2002) · PDF

E. Orlandini, A. Rechnitzer, S.G. Whittington
Random copolymers and the Morita approximation: polymer adsorption and polymer localization
J. Phys. A: Math. Gen., 35: 7729-7751 (2002) · PDF

M. Bousquet-Melou, A. Rechnitzer
Lattice animals and heaps of dimers
Discrete Math. 258: 235-274 (2002) · PDF

2001

E.J. Janse van Rensburg, A. Rechnitzer, M.S. Causo, S.G. Whittington
Self-averaging sequences in the statistical mechanics of random copolymers
J. Phys. A: Math. Gen., 34: 6381-6388 (2001) · PDF

E.J. Janse van Rensburg, A. Rechnitzer
Adsorbing and collapsing directed animals
Journal of Statistical Physics 105: 49-91 (2001) · PDF

A.L. Owczarek, A. Rechnitzer, L.H. Wong
Addendum to "On three-dimensional self-avoiding walk symmetry classes"
J. Phys. A: Math. Gen., 34: 6055-6060 (2001) · PDF

C. Chauve, S. Dulucq, A. Rechnitzer
Enumerating alternating trees
J. Combinatorial Theory: Series A, 94: 142-151 (2001) · PDF

2000

A.L. Owczarek, A. Rechnitzer
On three-dimensional self-avoiding walk symmetry classes
J. Phys. A: Math. Gen., 33: 2685-2723 (2000) · PDF

1999

M. Bousquet-Melou, A.J. Guttmann, W.P. Orrick, A. Rechnitzer
Inversion relations, reciprocity and polyominoes
Annal. Comb., 3: 223-249 (1999) · PDF

1997

A.L. Owczarek, A. Rechnitzer, R. Brak, A.J. Guttmann
On the hulls of directed percolation clusters
J. Phys. A: Math. Gen., 30: 6679-6691 (1997) · PDF

Conference Proceedings

M. Bouvel, V. Guerrini, A. Rechnitzer, S. Rinaldi
Semi-Baxter and strong-Baxter permutations
Séminaire Lotharingien de Combinatoire 78 (2017)

M.A. Bennett, A. Rechnitzer
Computing elliptic curves over Q: bad reduction at one prime
Proceedings of 2015 AMMCS-CAIMS Congress, Fields Institute Communications · PDF

A.L. Owczarek, R. Brak, A. Rechnitzer
Self-avoiding walks in slits and slabs with interactive walls
Journal of Mathematical Chemistry 45: 113-128 (2009) · PDF

R. Brak, A.L. Owczarek, A. Rechnitzer
Exact solutions of lattice polymer models
Journal of Mathematical Chemistry 45: 39-57 (2009) · PDF

E.J. Janse van Rensburg, T. Prellberg, A. Rechnitzer
Partially directed walks in a symmetric wedge
Proceedings of FPSAC 2007 · PDF

S. Corteel, R. Brak, A. Rechnitzer, J. Essam
A combinatorial derivation of the PASEP algebra
Proceedings of FPSAC 2005 · PDF

E.J. Janse van Rensburg, A. Rechnitzer
Exchange relations, Dyck paths and copolymer adsorption
Proceedings of FPSAC 2002

A. Rechnitzer
Haruspicy and non-D-finite functions
Proceedings of FPSAC 2001

M. Bousquet-Melou, A. Rechnitzer
Connected heaps are nice animals
Proceedings of FPSAC 1999

PhD Thesis

Haruspicy and anisotropic generating functions
PhD thesis, University of Melbourne [PDF] [PS.GZ]