Accepted | M.A. Bennett, G. Martin, K. O'Bryant, A. Rechnitzer Counting Zeros of Dirichlet L-Functions 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). |
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M.A. Bennett, A. Gherga, A. Rechnitzer Computing elliptic curves over Q Math. Comp. 88, 1341-1390 (2019) The pdf. Associated data and code |
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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). The pdf. On arxiv. Associated data and code |
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). On arXiv. |
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Y-B. 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 139--156 (2018). The pdf. On arXiv. |
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2017 | A.L. Owczarek and 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 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, 391-409 (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. |
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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. |
Y-B. Chan and A. Rechnitzer Accurate lower bounds on two-dimensional constraint capacities from corner transfer matrices IEEE Transactions on Information Theory 60: 3845-3858 (2014) The pdf. On arXiv. |
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M. Elder, A. Rechnitzer, E.J. Janse van Rensburg and T. Wong The cogrowth series for BS(N,N) is D-finite. International Journal of Algebra and Compuation. 24: 171-187 (2014). The pdf. On arXiv. Data from this paper:
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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. |
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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. |
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2012 | M. Elder, A. Rechnitzer and T. Wong On the cogrowth of Thompson's group F Groups, Complexity, and Cryptology. 4: 301-320 (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. |
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Y-B. Chan and A. Rechnitzer A Monte Carlo study of non-trapped self-avoiding walks J. Phys. A: Math. Theor. 45 405004 (2012) The pdf. |
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D. Gasumova, E. J. Janse van Rensburg and A. Rechnitzer Lattice knots in a slab J. Stat. Mech. Theo. Expr. P09004 (2012) The pdf. |
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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. |
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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: 1145-1171 (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 BFACF-style algorithms for polygons in the body-centered and face-centered cubic lattices J. Phys. A: Math. Theor. 44 165001 (2011) The pdf. On arXiv. |
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2010 | M. Elder and A. Rechnitzer Some geodesic problems for finitely generated groups. Groups, Complexity, Cryptology. 2: 223-229 (2010). On arXiv. |
M. Elder, É. Fusy and A. Rechnitzer Counting elements and geodesics in Thompson's group F Journal of Algebra. 324: 102-121 (2010). The pdf. Also on arXiv. |
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S. Cleary, M. Elder, A. Rechnitzer, J. Taback Random subgroups of Thompson's group F Groups, Geometry and Dynamics. 4: 91-126 (2010). The pdf. Also on arXiv. |
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2009 | J. Alvarez, M. Gara, E. J. Janse van Rensburg, and A. Rechnitzer Atmospheric Collapse in Self-Avoiding 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 self-avoiding 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 non-holonomic lattice walks in the quarter plane. Theoret. Comput. Sci. 410: 3616-3630 (2009). The pdf. Also on arXiv. |
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R. Brak, P. Dyke, J. Lee, A.L. Owczarek, T. Prellberg, A. Rechnitzer and S.G. Whittington A self-interacting partially directed walk subject to a force J. Phys. A: Math. Theor. 42 085001 (2009) The pdf. Also on arXiv. |
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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. |
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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. |
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A. L. Owczarek, T. Prellberg and A. Rechnitzer Finite-size scaling functions for directed polymers confined between attracting walls Journal of Physics A: Mathematical and Theoretical, 41, 035002 (2008). The pdf. Also on arXiv. |
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E.J. Janse van Rensburg, T. Prellberg and A. Rechnitzer Partially directed paths in a wedge. J. Combinatorial Theory - Series A, 115: 623-650 (2008). The submitted pdf. Also on arXiv. |
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2007 | A. L. Owczarek, A. Rechnitzer, T. Prellberg, and 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) 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, 14069-14084 (2007). Also on arXiv. |
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J. Krawczyk, A. L. Owczarek, T. Prellberg, and A. Rechnitzer A lattice model for parallel and orthogonal β-sheets using hydrogen-like bonding Physical Review E: 76, 051904 (2007) The pdf. Also on arXiv. Selected to appear in the Virtual Journal of Biological Physics Research. |
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R. Martin, E. Orlandini, A.L. Owczarek, A. Rechnitzer and 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. The pdf. |
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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, 4415-4437 (2007). The pdf. |
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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. |
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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 self-avoiding 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. |
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R. Brak, J. Essam, J. Osborn, A.L. Owczarek and A. Rechnitzer Lattice paths and the constant term. Journal of Physics: Conference Series, 42: 47-58, 2006. The submitted pdf. |
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A.L. Owczarek and A. Rechnitzer On the number of anisospiral walks: a challenge in numerical analysis.. Journal of Physics: Conference Series, 42: 225-230, 2006. The submitted pdf. |
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E.J. Janse van Rensburg, E. Orlandini, A.L. Owczarek, A. Rechnitzer and S.G. Whittington Self-avoiding walks in a slab with attractive walls. J. Phys. A: Math. Gen., 38: L823-828, 2005. The submitted pdf. |
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M.H. Albert, M. Elder, A. Rechnitzer, P. Westcott and M. Zabrocki On the Wilf-Stanley limit of 4231-avoiding permutations and a conjecture of Arratia. Advances in Applied Mathematics, 36: 96-105 (2006). The pdf. Also on arXiv. |
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A. Rechnitzer. Haruspicy 3: The anisotropic generasting function of directed bond-animals is not D-finite. J. Combinatorial Theory - Series A, 113: 1031-1049 (2006). The submitted pdf Also on arXiv. |
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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. The pdf. Also on arXiv |
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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. |
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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: 4309-4325, 2005. The pdf. |
A.J. Guttmann, R. Parviainen and A. Rechnitzer Self-avoiding walks and trails on the 3.122 lattice. J. Phys. A: Math. Gen., 38: 543-554, 2005. The submitted pdf. Also on arXiv. |
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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. |
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G. Iliev, A. Rechnitzer and S. G. Whittington, Localization of random copolymers and the Morita approximation. J. Phys. A: Math. Gen., 38: 1209-1223, 2005. The submitted pdf. |
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J. Krawczyk, T. Prellberg, A. L. Owczarek, and A. Rechnitzer, Layering transitions for adsorbing polymers in poor solvents. Europhys. Lett., 70: 726-732 (2005). The submitted pdf A slightly older version is on arXiv. |
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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 self-avoiding walks in two and three dimensions. J. Phys. A: Math. Gen., 37: 6875-6898, 2004. PDF |
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A. Rechnitzer and E.J. Janse van Rensburg. Exchange relations, Dyck paths and copolymer adsorption. Discrete Applied Mathematics, 150: 49-71, 2004. Not quite final PDF |
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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: 228-257, 2003. PDF |
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M. Bousquet-Mélou and A. Rechnitzer. The site-perimeter of bargraphs. Advances in Applied Mathematics, 31: 86-112, 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 self-avoiding walks. J. Phys. A; Math. Gen., 35:L605-L612, 2002. PDF |
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E. Orlandini, A. Rechnitzer, and S. G. Whittington. Random copolymers and the Morita approximation: polymer adsorption and polymer localization. J. Phys. A: Math. Gen., 35:7729-7751, 2002. PDF |
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M. Bousquet-Mélou and A. Rechnitzer. Lattice animals and heaps of dimers. Discrete Math., 258:235-274, 2002. PDF |
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2001 | E.J. Janse van Rensburg, A. Rechnitzer, M.S. Causo, and 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 and A. Rechnitzer. Adsorbing and collapsing directed animals. Journal of Statistical Physics , 105:49-91, 2001. PDF |
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A.L. Owczarek, A. Rechnitzer, and L. H. Wong. Addendum to "On three-dimensional self-avoiding walk symmetry classes". J. Phys. A: Math. Gen., 34:6055-6060, 2001. PDF |
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C. Chauve, S. Dulucq, and A. Rechnitzer. Enumerating alternating trees. J. Combinatorial Theory: Series A, 94:142-151, 2001. PDF |
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2000 | A. L. Owczarek and A. Rechnitzer. On three-dimensional self-avoiding walk symmetry classes. J. Phys. A: Math. Gen., 33:2685-2723, 2000. PDF |
1999 | M. Bousquet-Mélou, A. J. Guttmann, W. P. Orrick, and A. Rechnitzer. Inversion relations, reciprocity and polyominoes. Annal Comb., 3:223-249, 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., 30:6679-6691, 1997. PDF |