Accepted  M.A. Bennett, G. Martin, K. O'Bryant, A. Rechnitzer Counting Zeros of Dirichlet LFunctions Accepted for publication in Mathematics of Computation. The pdf. On arxiv Associated code 
2019  H. Chapman, A. Rechnitzer A Markov chain sampler for plane curves The pdf. On arxiv Experimental Mathematics (published online September 2019). 
N.R. Beaton, A.L. Owczarek, A. Rechnitzer Exact solution of some quarter plane walks with interacting boundaries The pdf. On Arxiv. Electronic Journal of Combinatorics 26, P3.53 (2019). 

M.A. Bennett, A. Gherga, A. Rechnitzer Computing elliptic curves over Q Math. Comp. 88, 13411390 (2019) The pdf. Associated data and code 

2018  M.A. Bennett, G. Martin, K. O'Bryant, A. Rechnitzer Explicit bounds for primes in arithmetic progressions Illinois J. Math. Volume 62, Number 14, 427532 (2018). The pdf. On arxiv. Associated data and code 
M. Bouvel, V. Guerrini, A. Rechnitzer, S. Rinaldi SemiBaxter and strongBaxter: two relatives of the Baxter sequence SIAM J Discrete Math 32, pp. 27952819 (2018). On arXiv. 

YB. Chan and 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 139156 (2018). The pdf. On arXiv. 

2017  A.L. Owczarek and A. Rechnitzer Force signature of the unzipping transition for strip confined twodimensional polymers J. Phys. A: Math. Theor. 50, 484001 (2017)  selected for the journal's Highlights of 2017collection The pdf. 
2016  R. Tabbara, A.L. Owczarek and A. Rechnitzer An exact solution of three interacting friendly walks in the bulk J. Phys. A: Math. Theor. 49, 154004 (2016) On arXiv. 
2015  M. Elder, A. Rechnitzer and E.J. Janse van Rensburg Random sampling of trivials words in finitely presented groups Experimental Mathematics 24, 391409 (2015) The pdf. On 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) The pdf. On 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). The pdf. On arXiv. 
YB. Chan and A. Rechnitzer Accurate lower bounds on twodimensional constraint capacities from corner transfer matrices IEEE Transactions on Information Theory 60: 38453858 (2014) The pdf. On arXiv. 

M. Elder, A. Rechnitzer, E.J. Janse van Rensburg and T. Wong The cogrowth series for BS(N,N) is Dfinite. International Journal of Algebra and Compuation. 24: 171187 (2014). The pdf. On arXiv. Data from this paper:


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). The pdf. 

2013  M. Elder, A. Rechnitzer, E.J. Janse van Rensburg and T. Wong On trivial words in finitely presented groups. This article has been rewritten and submitted as two separate papers arXiv:1309.4184 (accepted for publication in IJAC) and arXiv:1312.5722 (submitted). 
S. Cleary, A. Rechnitzer and T. Wong Common edges in rooted trees and polygonal triangulations Electronic Journal of Combinatorics. 20: P39 (2013) The pdf. 

2012  M. Elder, A. Rechnitzer and T. Wong On the cogrowth of Thompson's group F Groups, Complexity, and Cryptology. 4: 301320 (2012) The pdf. On arXiv. 
A.L. Owczarek, A. Rechnitzer and 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) The pdf. On arXiv. 

YB. Chan and A. Rechnitzer A Monte Carlo study of nontrapped selfavoiding walks J. Phys. A: Math. Theor. 45 405004 (2012) The pdf. 

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

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

2011  E.J. Janse van Rensburg and A. Rechnitzer Minimal knotted polygons in cubic lattices Journal of Statistical Mechanics: Theory and Experiment: P09008 (2011). The pdf. On arXiv. See here for data associated with this paper. 
E.J. Janse van Rensburg and A. Rechnitzer Generalised atmospheric sampling of knotted polygons Journal of Knot Theory and Its Ramifications. 20: 11451171 (2011) The pdf. 

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

E.J. Janse van Rensburg and A. Rechnitzer BFACFstyle algorithms for polygons in the bodycentered and facecentered cubic lattices J. Phys. A: Math. Theor. 44 165001 (2011) The pdf. On arXiv. 

2010  M. Elder and A. Rechnitzer Some geodesic problems for finitely generated groups. Groups, Complexity, Cryptology. 2: 223229 (2010). On arXiv. 
M. Elder, É. Fusy and A. Rechnitzer Counting elements and geodesics in Thompson's group F Journal of Algebra. 324: 102121 (2010). The pdf. Also on arXiv. 

S. Cleary, M. Elder, A. Rechnitzer, J. Taback Random subgroups of Thompson's group F Groups, Geometry and Dynamics. 4: 91126 (2010). The pdf. Also on arXiv. 

2009  J. Alvarez, M. Gara, E. J. Janse van Rensburg, and A. Rechnitzer Atmospheric Collapse in SelfAvoiding Walks: A Numerical Study using GARM Journal of Statistical Mechanics: Theory and Experiment: P12005 (2009). The pdf. 
E.J. Janse van Rensburg and A. Rechnitzer Generalised atmospheric sampling of selfavoiding walks J. Phys. A: Math. Theor. 42: 335001 (2009). The pdf. 

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

M. Mishna and A. Rechnitzer Two nonholonomic lattice walks in the quarter plane. Theoret. Comput. Sci. 410: 36163630 (2009). The pdf. Also on arXiv. 

R. Brak, P. Dyke, J. Lee, A.L. Owczarek, T. Prellberg, A. Rechnitzer and S.G. Whittington A selfinteracting partially directed walk subject to a force J. Phys. A: Math. Theor. 42 085001 (2009) The pdf. Also on arXiv. 

2008  A. Rechnitzer and E.J. Janse van Rensburg Generalised Atmospheric Rosenbluth Methods (GARM) Journal of Physics A: Mathematical and Theoretical (Fast Track Communications), 41, 442002, (2008). The pdf. Also on arXiv. 
I. Jensen and A. Rechnitzer Exact perimeter generating function for a model of punctured staircase polygons. Journal of Physics A: Mathematical and Theoretical, 41, 215002, (2008). The pdf. 

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

A. L. Owczarek, T. Prellberg and A. Rechnitzer Finitesize scaling functions for directed polymers confined between attracting walls Journal of Physics A: Mathematical and Theoretical, 41, 035002 (2008). The pdf. Also on arXiv. 

E.J. Janse van Rensburg, T. Prellberg and A. Rechnitzer Partially directed paths in a wedge. J. Combinatorial Theory  Series A, 115: 623650 (2008). The submitted pdf. Also on arXiv. 

2007  A. L. Owczarek, A. Rechnitzer, T. Prellberg, and J. Krawczyk On the location of the surfaceattached globule phase in collapsing polymers Journal of Physics A: Mathematical and Theoretical, 40, 1325713267 (2007) The pdf. Also on arXiv. 
E.J. Janse van Rensburg, T. Prellberg and A. Rechnitzer Directed paths in a wedge Journal of Physics A: Mathematical and Theoretical, 40, 1406914084 (2007). Also on arXiv. 

J. Krawczyk, A. L. Owczarek, T. Prellberg, and A. Rechnitzer A lattice model for parallel and orthogonal βsheets using hydrogenlike bonding Physical Review E: 76, 051904 (2007) The pdf. Also on arXiv. Selected to appear in the Virtual Journal of Biological Physics Research. 

R. Martin, E. Orlandini, A.L. Owczarek, A. Rechnitzer and S.G. Whittington Exact enumeration and Monte Carlo results for selfavoiding walks in a slab Journal of Physics A: Mathematical and theoretical, 40, 75097521, 2007. The pdf. 

R. Brak, G.K. Iliev, A. Rechnitzer and S.G. Whittington Motzkin path models of long chain polymers in slits Journal of Physics A: Mathematical and Theoretical, 40, 44154437 (2007). The pdf. 

Y. Chan, A.L. Owczarek, A. Rechnitzer and G. Slade Mean unknotting times of random knots and embeddings. Journal of statistical mechanics: theory and experiment, P05004, 2007 The pdf. 

2006 
R. Brak, S. Corteel, J. Essam, R. Parviainen and A. Rechnitzer A Combinatorial derivation of the PASEP stationary state. Electronic Journal of Combinatorics, 13: R108, 2006. The submitted pdf. 
J. Krawczyk, T. Prellberg, A. L. Owczarek, and A. Rechnitzer, On a type of selfavoiding random walk with multiple site weightings and restrictions. Physical Review Letters, 96: 240603 (2006). The submitted pdf. Selected to appear in the Virtual Journal of Biological Physics Research. 

R. Brak, J. Essam, J. Osborn, A.L. Owczarek and A. Rechnitzer Lattice paths and the constant term. Journal of Physics: Conference Series, 42: 4758, 2006. The submitted pdf. 

A.L. Owczarek and A. Rechnitzer On the number of anisospiral walks: a challenge in numerical analysis.. Journal of Physics: Conference Series, 42: 225230, 2006. The submitted pdf. 

E.J. Janse van Rensburg, E. Orlandini, A.L. Owczarek, A. Rechnitzer and S.G. Whittington Selfavoiding walks in a slab with attractive walls. J. Phys. A: Math. Gen., 38: L823828, 2005. The submitted pdf. 

M.H. Albert, M. Elder, A. Rechnitzer, P. Westcott and M. Zabrocki On the WilfStanley limit of 4231avoiding permutations and a conjecture of Arratia. Advances in Applied Mathematics, 36: 96105 (2006). The pdf. Also on arXiv. 

A. Rechnitzer. Haruspicy 3: The anisotropic generasting function of directed bondanimals is not Dfinite. J. Combinatorial Theory  Series A, 113: 10311049 (2006). The submitted pdf Also on arXiv. 

A. Rechnitzer. Haruspicy 2: The anisotropic generating function of selfavoiding polygons is not Dfinite. J. Combinatorial Theory  Series A, 113: 520546, 2006. The pdf. Also on arXiv 

T. Prellberg, J. Krawczyk, and A. Rechnitzer Polymer simulations with a flat histogram stochastic growth algorithm, In Computer Simulation Studies in Condensed Matter Physics XVII, Springer Verlag, 2006. The submitted pdf. Also on arXiv. 

2005 
R. Brak, A.L. Owczarek, A. Rechnitzer and S.G. Whittington A directed walk model of a long chain polymer in a slit with attractive walls. J. Phys. A: Math. Gen., 38: 43094325, 2005. The pdf. 
A.J. Guttmann, R. Parviainen and A. Rechnitzer Selfavoiding walks and trails on the 3.12^{2} lattice. J. Phys. A: Math. Gen., 38: 543554, 2005. The submitted pdf. Also on arXiv. 

J. Krawczyk, T. Prellberg, A. L. Owczarek, and A. Rechnitzer, Pulling adsorbing and collapsing polymers from a surface. J. Stat. Mech.: Theor. Exp. P05008, 2005. The submitted pdf. A slightly older version is on arXiv. 

G. Iliev, A. Rechnitzer and S. G. Whittington, Localization of random copolymers and the Morita approximation. J. Phys. A: Math. Gen., 38: 12091223, 2005. The submitted pdf. 

J. Krawczyk, T. Prellberg, A. L. Owczarek, and A. Rechnitzer, Layering transitions for adsorbing polymers in poor solvents. Europhys. Lett., 70: 726732 (2005). The submitted pdf A slightly older version is on arXiv. 

2004  J. Krawczyk, T. Prellberg, A. Rechnitzer and A.L. Owczarek Stretching of a chain polymer adsorbed at a surface J. Stat. Mech.: Theor. Exp. (2004) P10004 PDF. Also on arXiv. 
E.J. Janse van Rensburg and A. Rechnitzer. Multiple Markov chain Monte Carlo study of adsorbing selfavoiding walks in two and three dimensions. J. Phys. A: Math. Gen., 37: 68756898, 2004. PDF 

A. Rechnitzer and E.J. Janse van Rensburg. Exchange relations, Dyck paths and copolymer adsorption. Discrete Applied Mathematics, 150: 4971, 2004. Not quite final PDF 

2003  E.J. Janse van Rensburg and 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: 228257, 2003. PDF 

M. BousquetMélou and A. Rechnitzer. The siteperimeter of bargraphs. Advances in Applied Mathematics, 31: 86112, 2003. PDF  
2002  E. J. Janse van Rensburg and A. Rechnitzer. Exchange symmetries in motzkin paths and bargraph models of copolymer adsorption. Electronic Journal of Combinatorics , 9, 2002. PDF 
A. Rechnitzer and E. J. Janse van Rensburg. Canonical Monte Carlo determination of the connective constant of selfavoiding walks. J. Phys. A; Math. Gen., 35:L605L612, 2002. PDF 

E. Orlandini, A. Rechnitzer, and S. G. Whittington. Random copolymers and the Morita approximation: polymer adsorption and polymer localization. J. Phys. A: Math. Gen., 35:77297751, 2002. PDF 

M. BousquetMélou and A. Rechnitzer. Lattice animals and heaps of dimers. Discrete Math., 258:235274, 2002. PDF 

2001  E.J. Janse van Rensburg, A. Rechnitzer, M.S. Causo, and S.G. Whittington. Selfaveraging sequences in the statistical mechanics of random copolymers. J. Phys. A: Math. Gen. , 34:63816388, 2001. PDF 
E. J. Janse van Rensburg and A. Rechnitzer. Adsorbing and collapsing directed animals. Journal of Statistical Physics , 105:4991, 2001. PDF 

A.L. Owczarek, A. Rechnitzer, and L. H. Wong. Addendum to "On threedimensional selfavoiding walk symmetry classes". J. Phys. A: Math. Gen., 34:60556060, 2001. PDF 

C. Chauve, S. Dulucq, and A. Rechnitzer. Enumerating alternating trees. J. Combinatorial Theory: Series A, 94:142151, 2001. PDF 

2000  A. L. Owczarek and A. Rechnitzer. On threedimensional selfavoiding walk symmetry classes. J. Phys. A: Math. Gen., 33:26852723, 2000. PDF 
1999  M. BousquetMélou, A. J. Guttmann, W. P. Orrick, and A. Rechnitzer. Inversion relations, reciprocity and polyominoes. Annal Comb., 3:223249, 1999. PDF 
1997  A. L. Owczarek, A. Rechnitzer, R. Brak and A. J. Guttmann. On the hulls of directed percolation clusters. J. Phys. A: Math. Gen., 30:66796691, 1997. PDF 