W. Moore, R. Brak. Biorthogonal Polynomial Sequences and the Asymmetric Simple Exclusion Process. 2019.
J. Foxcroft, R. Brak. Combinatorial enumeration and the Bethe Ansatz. 2017.
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, 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, Bousquet-Melou. Polygons, Polyominoes and Polycubes. 43-76, Springer Science+Business Media, 2009.
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.
S Corteel, R. Brak, A Rechnitzer, J Essam. A combinatorial derivation of the PASEP stationary state. FPSAC Proceedings 2005 - 17th Annual International Conference on Formal Power Series and Algebraic Combinatorics, 555-565, 2005.
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, 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.
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.
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, JW Essam. Directed compact percolation near a wall: III. Exact results for the mean length and number of contacts. Journal of Physics A: Mathematical and Theoretical, 32, 355-367, 1999. doi: 10.1088/0305-4470/32/2/010.
R. Brak, J. Essam, A. Owczarek. Partial Difference equation method for lattice path problems. Annals of Comb., 3, 265--275, 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. 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, 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. 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, 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.
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.
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.
FM Bhatti, R. Brak, JW Essam, T Lookman. Series expansion analysis of the backbone properties of two-dimensional percolation clusters. Journal of Physics A: Mathematical and Theoretical, 30, 6215-6232, 1997. doi: 10.1088/0305-4470/30/18/008.
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.
T Prellberg, R. Brak. Critical exponents from nonlinear functional equations for partially directed cluster models. Journal of Statistical Physics, 78, 701-730, 1995. doi: 10.1007/BF02183685.
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.
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.
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.
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.
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. The Tricritical Behaviour of Self-Interacting Partially Directed Walks. J. Stat. Phys., 72, 737-772, 1993. doi: 10.1007/BF01048031. 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. Reply to Exact Scaling Form for the 2D Polymer Phase. Phys. Rev. Lett., 71, 4275, 1993. 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.
A. Owczarek, T. Prellberg, R. Brak. A New Scaling Form for the Collapsed Polymer Phase. Phys. Rev. Lett., 70, 951--953, 1993. 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. 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.
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. 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, RJ Elliott. Correlated tracer diffusion in a disordered medium. Materials Science and Engineering: B, 3, 159-162, 1989. doi: 10.1016/0921-5107(89)90196-7.