Publication List

    Textbooks

    • CLP Calculus textbook sequence written with Joel Feldman and Elyse Yeager.
    • The texts are all freely available at the CLP homepage.

    Journal Articles

    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).
    M.A. Bennett, A. Gherga, A. Rechnitzer
    Computing elliptic curves over Q
    Math. Comp. 88, 1341-1390 (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 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.
    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.
    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 2017 collection
    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.
    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.
    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:
    • algebraic equations for G(z,q) for BS(N,N) for N=1..10
    • differential equations for cogrowth series of BS(N,N) for N=1, N=2, N=3, N=4, N=5.
    A big thanks to Manuel Kauers for help with these DE's.
    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: 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.
    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.
    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: 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.
    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.
    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.
    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.
    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.
    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
    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.
    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.
    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.
    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.
    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.
    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.
    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 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.
    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.
    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.
    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.
    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.
    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.
    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
    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: 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.
    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: 1209-1223, 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: 726-732 (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 self-avoiding walks in two and three dimensions.
    J. Phys. A: Math. Gen., 37: 6875-6898, 2004. PDF
    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
    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
    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
    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
    M. Bousquet-Mélou and 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, 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
    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
    C. Chauve, S. Dulucq, and A. Rechnitzer.
    Enumerating alternating trees.
    J. Combinatorial Theory: Series A, 94:142-151, 2001. PDF
    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

    In conference proceedings

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

    • A.L. Owczarek, R. Brak and A. Rechnitzer
      Self-avoiding walks in slits and slabs with interactive walls
      Journal of Mathematical Chemistry, 45: 113-128 (2009). The PDF.
      Lattices and trajectories: A symposium of mathematical chemistry in honour of Ray Kapral and Stu Whittington

    • R. Brak, A.L. Owczarek and A. Rechnitzer
      Exact solutions of lattice polymer models
      Journal of Mathematical Chemistry, 45: 39-57 (2009).. The PDF.
      Lattices and trajectories: A symposium of mathematical chemistry in honour of Ray Kapral and Stu Whittington

    • E.J. Janse van Rensburg, T. Prellberg and A. Rechnitzer.
      Partially directed walks in a symmetric wedge.
      Published in the Proceedings of FPSAC 2007. The PDF.

    • S. Corteel, R. Brak, A. Rechnitzer and J. Essam.
      A combinatorial derivation of the PASEP algebra.
      Published in the Proceedings of FPSAC 2005. The PDF.

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

    • A. Rechnitzer.
      Haruspicy and non-D-finite functions
      Published in the Proceedings of FPSAC 2001.

    • M. Bousquet-Mélou and A. Rechnitzer.
      Connected heaps are nice animals
      Published in the Proceedings of FPSAC 1999.

    My PhD thesis

    • .PS.GZ and .PDF