Publications

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  • R. Brak, W. Moore. Bi-orthogonal polynomial sequences and the asymmetric simple exclusion process. Journal of Physics A: Mathematical and Theoretical, 48, 315205 (15pp), 2015. doi: 10.1088/1751-8113/48/31/315205.

  • R. Brak, W. Galleas. Constant term solution for an arbitrary number of osculating lattice paths. Letters in Mathematical Physics, 103, 1261-1272, 2013. doi: 10.1007/s11005-013-0646-1.

  • R. Brak, J Essam. Simple Asymmetric Exclusion Model and Lattice Paths: Bijections and Involutions. Journal of Physics A - Mathematical and Theoretical, 45, 494007 (22pp), 2012. doi: 10.1088/1751-8113/45/49/494007.

  • R. Brak, G. Iliev, T. Prellberg. An Infinite Family of Adsorption Models and Restricted Lukasiewicz Paths. Journal of Statistical Physics, 145, 669-685, 2011. doi: 10.1007/s10955-011-0306-8.

  • R. Brak, G. Iliev, A. Owczarek, S. Whittington. The exact solution of a three-dimensional lattice polymer confined in a slab with sticky walls. J. Phys. A: Math. Theor., 43, 135001 (12pp), 2010. doi: 10.1088/1751-8113/43/13/135001. PDF.

  • Mireille Bousquet-Melou, R. Brak, M Bousquet-Mélou. Exactly Solved Models. Polygons, Polyominoes and Polycubes, 775, 43-78, 2009. doi: 10.1007/978-1-4020-9927-4_3.

  • R. Brak, Bousquet-Melou. Polygons, Polyominoes and Polycubes. 43-76, Springer Science+Business Media, 2009.

  • R. Brak, Osborn. Chebyshev Type Lattice path weight polynomials by a constant term method. Journal of Physics A - Mathematical and Theoretical, 42, 445201 (21pp), 2009. doi: 10.1088/1751-8113/42/44/445201.

  • R. Brak, P. Dyke, J. Lee, A. Owczarek, T. Prellberg, A. Rechnitzer, S. Whittington. A self-interacting partially directed walk subject to a force. J. Phys. A: Math. Theor., 42, 085001 (30pp), 2009. doi: 10.1088/1751-8113/42/8/085001. arXiv.

  • H. Lonsdale, R. Brak, John Essam, A. Owczarek, A. Rechnitzer. On directed compact percolation near a damp wall. Journal of Physics A - Mathematical and Theoretical, 42, 1-26, 2009. doi: 10.1088/1751-8113/42/12/125001. PDF.

  • A. Owczarek, R. Brak, A. Rechnitzer. Self-avoiding walks in slits and slabs with interactive walls. J. Math. Chem., 45, 113-128, 2008. doi: 10.1007/s10910-008-9371-x. PDF.

  • R. Brak, A. Owczarek, A. Rechnitzer. Exact solutions of some lattice polymer models. J. Math. Chem., 45, 39-57, 2008. doi: 10.1007/s10910-008-9366-7. PDF.

  • R. Brak, G. Iliev, A. Rechnitzer, S. Whittington. Motzkin path models of long chain polymers in slits. Journal of Physics A - Mathematical and Theoretical, 40, 4415-4437, 2007. doi: 10.1088/1751-8113/40/17/001.

  • R. Brak, S Corteel, J Essam, R. Parviainen, A. Rechnitzer. A combinatorial derivation of the PASEP stationary state. Electronic Journal of Combinatorics, 13, 1-23, 2006.

  • R. Brak, Sylvie Corteel, John Essam, Robert Parviainen, Andrew Rechnitzer. A combinatorial derivation of the PASEP stationary state. Electronic Journal of Combinatorics, 13, 1 (23pp), 2006.

  • R. Brak, J. W. Essam, J. Osborn, A. Owczarek, A. Rechnitzer. Lattice Paths and the Constant Term. Journal of Physics - Conference Series, 42, 47-58, 2006. doi: 10.1088/1742-6596/42/1/006. PDF.

  • R. Brak, A. Owczarek, A. Rechnitzer, S. Whittington. A directed walk model of a long chain polymer in a slit with attractive walls. J. Phys. A, 38, 4309-4325, 2005. doi: 10.1088/0305-4470/38/20/001. arXiv.

  • R. Brak, W Essam, J. ESSAM. Asymmetric exclusion model and weighted lattice paths. Journal of Physics A - Mathematical and General, 37, 4183-4217, 2004. doi: 10.1088/0305-4470/37/14/002. PDF.

  • R. Brak, J. de Gier, V. Rittenberg. Nonequilibrium stationary states and equilibrium models with long range interactions. J. Phys. A: Math. Gen., 37, 4303-4320, 2004. doi: 10.1088/0305-4470/37/15/001. PDF.

  • R. Brak, JW Essam. Bicoloured Dyck paths and the contact polynomial for n non-intersecting paths in a half-plane lattice. Electronic Journal of Combinatorics, 10, 2003.

  • R. Brak, JW Essam. Bicoloured Dyck paths and the contact polynomial forn non-intersecting paths in a half-plane lattice. Electronic Journal of Combinatorics, 10, 1-18, 2003.

  • A. C. Oppenheim, R. Brak, A. Owczarek. Anisotropic step, mutual contact and area weighted festoons and parallelogram polyominoes on the triangular lattice. J. Phys. A., 35, 3213-3230, 2002. doi: 10.1088/0305-4470/35/14/305. PDF.

  • A. C. Oppenheim, R. Brak, A. Owczarek. Anisotropic step, surface contact, and area weighted directed walks on the triangular lattice. Int. J. Mod. Phys. B, 16, 1269-1299, 2002. doi: 10.1142/S0217979202010087. PDF.

  • R. Brak, W Essam, JW Essam. return polynomials for non-intersecting paths above a surface on the directed square lattice. Journal of Physics A - Mathematical and General, 34, 10763-10782, 2001. doi: 10.1088/0305-4470/34/49/303. PDF.

  • A. Owczarek, J. Essam, R. Brak. Scaling analysis for the adsorption transition in a watermelon network of $n$ directed non-intersecting walks. J. Stat. Phys., 102, 997-1017, 2001. doi: 10.1023/A:1004819507352. PDF.

  • R. Brak, J. Essam, A. Owczarek. From the Bethe Ansatz to the Gessel-Viennot Theorem. Annals of Comb., 3, 251-263, 1999. PDF.

  • R. Brak, JW Essam, A. Owczarek. From the Bethe Ansatz to the Gessel-Viennot theorem. Annals of Combinatorics, 3, 251-263, 1999. doi: 10.1007/BF01608786.

  • R. Brak, JW Essam, A. Owczarek. Partial difference equation method for lattice path problems. Annals of Combinatorics, 3, 265-275, 1999. doi: 10.1007/BF01608787.

  • R. Brak, J. Essam, A. Owczarek. Exact solution of N directed non-intersecting walks interacting with one or two boundaries. J. Phys. A., 32, 2921-2929, 1999. doi: 10.1088/0305-4470/32/16/003. PDF.

  • R. Brak, J. Essam , A. Owczarek. Equivalence of the Bethe Ansatz and the Gessel-Viennot Theorem for Non-intersecting Paths. 108--118, Proceedings of the 11th Formal Power Series and Algebraic Combinatorics Conference, 1999. PDF.

  • R. Brak, A. Owczarek. A combinatorial interpretation of the free-fermion condition of the six-vertex model. J. Phys. A., 32, 3497-3503, 1999. doi: 10.1088/0305-4470/32/19/303. arXiv.

  • R. Brak, J. Essam, A. Owczarek. Partial Difference equation method for lattice path problems. Annals of Comb., 3, 265--275, 1999. PDF.

  • R. Brak, J. W. Essam. Directed Percolation near a wall: III. Excact results for the mean length and number of contacts. J. Phys. A., 31, 4851-4869, 1999. PDF.

  • R. Brak, A. Owczarek, C. Soteros. On Anisotropic Spiral Self-avoiding Walks. J. Phys. A., 31, 4851-4869, 1998. doi: 10.1088/0305-4470/31/21/005. PDF.

  • R. Brak, P. P. Nidras, A. Owczarek. Cluster Structure of Collapsing Polymers. J. Stat. Phys., 91, 75-93, 1998. doi: 10.1023/A:1023083903287. PDF.

  • R. Brak, J. Essam, A. Owczarek. New Results for Directed Vesicles and Chains near an Attractive Wall. J. Stat. Phys., 93, 155-192, 1998. doi: 10.1023/B:JOSS.0000026731.35385.93. PDF.

  • A. Owczarek, A. Rechnitzer, R. Brak, A. Guttmann. On the Hulls of Directed Percolation Clusters. J. Phys. A., 30, 6679-6691, 1997. doi: 10.1088/0305-4470/30/19/011. PDF.

  • R. Brak. Osculating lattice paths and alternating sign matrices. Formal Power Series and Alegebraic Combinatorics, 9th Conference, 1997. PDF.

  • R. Brak, A. Owczarek. On the Analyticity Properties of Scaling Functions in Models of Polymer Collapse. J. Phys. A., 28, 4709-4725, 1995. doi: 10.1088/0305-4470/28/17/007. PDF.

  • D. Bennett-Wood, R. Brak, A. Guttmann, A. Owczarek, T. Prellberg. Low Temperature Partition Function Scaling: Series Analysis Results. J. Phys. A., 27, L1-L8, 1994. doi: 10.1088/0305-4470/27/2/001. PDF.

  • R. Brak, A. Owczarek, T. Prellberg. Exact Scaling Behaviour of Partially Convex Vesicles. J. Stat. Phys., 76, 1101-1128, 1994. doi: 10.1007/BF02187057. PDF.

  • A. Owczarek, T. Prellberg, R. Brak. New Scaling Form for the Collapsed Polymer Phase. Physical Review Letters, 70, 951-953, 1993. doi: 10.1103/PhysRevLett.70.951.

  • A. Owczarek, T. Prellberg, R. Brak. Exact Scaling Form for the Collapsed 2D Polymer Phase - Reply. Physical Review Letters, 71, 4275 (1pp), 1993. doi: 10.1103/PhysRevLett.71.4275.

  • AR Conway, R. Brak, A. Guttmann. Directed animals on two-dimensional lattices. Journal of Physics A: Mathematical and General, 26, 3085-3091, 1993. doi: 10.1088/0305-4470/26/13/013.

  • A. Owczarek, T. Prellberg, R. Brak. A New Scaling Form for the Collapsed Polymer Phase. Phys. Rev. Lett., 70, 951--953, 1993. PDF.

  • A. Owczarek, T. Prellberg, R. Brak. Reply to Exact Scaling Form for the 2D Polymer Phase. Phys. Rev. Lett., 71, 4275, 1993. PDF.

  • T. Prellberg, A. Owczarek, R. Brak, A. Guttmann. Finite Length Scaling of Collapsing Directed Walks. Phys. Rev. E., 48, 2386-2396, 1993. doi: 10.1103/PhysRevE.48.2386. PDF.

  • A. Owczarek, T. Prellberg, R. Brak. The Tricritical Behaviour of Self-Interacting Partially Directed Walks. J. Stat. Phys., 72, 737-772, 1993. doi: 10.1007/BF01048031. PDF.

  • R. Brak, A. Owczarek, T. Prellberg. A Scaling Theory of Collapse Transitions. J. Phys. A., 26, 4565-4579, 1993. doi: 10.1088/0305-4470/26/18/022. PDF.

  • R. Brak, A. Guttmann, S. Whittington. A collapse transition in a directed walk model. Journal of Physics A: Mathematical and General, 25, 2437-2446, 1992. doi: 10.1088/0305-4470/25/9/017.

  • R. Brak, A. Guttmann, S. Whittington. On the behaviour of collapsing linear and branched polymers. Journal of Mathematical Chemistry, 8, 255-267, 1991. doi: 10.1007/BF01166941.

  • R. Brak, A. Guttmann. Exact solution of the staircase and row-convex polygon perimeter and area generating function. Journal of Physics A: Mathematical and General, 23, 4581-4588, 1990. doi: 10.1088/0305-4470/23/20/019.

  • R. Brak, A. Guttmann, I. Enting . Exact solution of the row-convex polygon perimeter generating function. Journal of Physics A: Mathematical and General, 23, 2319-2326, 1990. doi: 10.1088/0305-4470/23/12/016.

  • R. Brak, A. Guttmann. Algebraic approximants: A new method of series analysis. Journal of Physics A: General Physics, 23, L1331-L1337, 1990. doi: 10.1088/0305-4470/23/24/008.