R Brak

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All published works

Action	Title	Year	Authors
+	Weyl chambers for short step Quarter-plane Lattice Paths	2020	R Brak
+	Bi-orthogonal Polynomials and the Five parameter Asymmetric Simple Exclusion Process	2019	R Brak W. Frank Moore
+	Fibonacci, Motzkin, Schroder, Fuss-Catalan and other Combinatorial Structures: Universal and Embedded Bijections	2019	R Brak N. Mahony
+	A Universal Bijection for Catalan Structures	2018	R Brak
+	A Universal Bijection for Catalan Structures	2018	R Brak
+ PDF Chat	Bi-orthogonal polynomial sequences and the asymmetric simple exclusion process	2015	R Brak W. Frank Moore
+ PDF Chat	Constant Term Solution for an Arbitrary Number of Osculating Lattice Paths	2013	R Brak W. Galléas
+ PDF Chat	Simple asymmetric exclusion model and lattice paths: bijections and involutions	2012	R Brak J W Essam
+ PDF Chat	An Infinite Family of Adsorption Models and Restricted Lukasiewicz Paths	2011	R Brak G K Iliev Thomas Prellberg
+	The exact solution of a three-dimensional lattice polymer confined in a slab with sticky walls	2010	R Brak G K Iliev A L Owczarek S G Whittington
+ PDF Chat	Chebyshev type lattice path weight polynomials by a constant term method	2009	R Brak Judy-anne H. Osborn
+ PDF Chat	On directed compact percolation near a damp wall	2009	H Lonsdale R Brak J W Essam A L Owczarek Andrew Rechnitzer
+ PDF Chat	A self-interacting partially directed walk subject to a force	2009	R Brak Patrick Dyke J Lee A L Owczarek Thomas Prellberg Andrew Rechnitzer S G Whittington
+	Exactly Solved Models	2009	Mireille Bousquet‐Mélou R Brak
+ PDF Chat	Exactly solved models of polyominoes and polygons	2009	Mireille Bousquet‐Mélou R Brak
+ PDF Chat	Polygons, Polyominoes and Polycubes	2009	Mireille Bousquet‐Mélou R Brak
+	Exact solutions of lattice polymer models	2008	R Brak A L Owczarek Andrew Rechnitzer
+	A self-interacting partially directed walk subject to a force	2008	R Brak Patrick Dyke J. Lee A L Owczarek Thomas Prellberg Andrew Rechnitzer S G Whittington
+	Motzkin path models of long chain polymers in slits	2007	R Brak G K Iliev Andrew Rechnitzer S G Whittington
+ PDF Chat	A Combinatorial Derivation of the PASEP Stationary State	2006	R Brak Sylvie Corteel J W Essam Robert Parviainen Andrew Rechnitzer
+ PDF Chat	Lattice Paths and the Constant Term	2006	R Brak J W Essam Judy-anne H. Osborn A L Owczarek Andrew Rechnitzer
+ PDF Chat	A directed walk model of a long chain polymer in a slit with attractive walls	2005	R Brak A L Owczarek Andrew Rechnitzer S G Whittington
+ PDF Chat	Nonequilibrium stationary states and equilibrium models with long range interactions	2004	R Brak Jan de Gier V. Rittenberg
+ PDF Chat	Asymmetric exclusion model and weighted lattice paths	2004	R Brak J W Essam
+ PDF Chat	Bicoloured Dyck Paths and the Contact Polynomial for $n$ Non-Intersecting Paths in a Half-Plane Lattice	2003	R Brak J W Essam
+	ANISOTROPIC STEP, SURFACE CONTACT, AND AREA WEIGHTED DIRECTED WALKS ON THE TRIANGULAR LATTICE	2002	Amotz Oppenheim R Brak A L Owczarek
+	Anisotropic step, mutual contact and area weighted festoons and parallelogram polyominoes on the triangular lattice	2002	Amotz Oppenheim R Brak A L Owczarek
+	Return polynomials for non-intersecting paths above a surface on the directed square lattice	2001	R Brak J W Essam
+	From the Bethe Ansatz to the Gessel-Viennot Theorem	2000	R Brak J W Essam A L Owczarek
+ PDF Chat	From the Bethe Ansatz to the Gessel-Viennot theorem	1999	R Brak J W Essam A L Owczarek
+ PDF Chat	Partial difference equation method for lattice path problems	1999	R Brak J W Essam A L Owczarek
+ PDF Chat	Directed compact percolation near a wall: III. Exact results for the mean length and number of contacts	1999	R Brak J W Essam
+	Exact solution of<i>N</i>directed non-intersecting walks interacting with one or two boundaries	1999	R Brak J W Essam A L Owczarek
+ PDF Chat	A combinatorial interpretation of the free-fermion condition of the six-vertex model	1999	R Brak A L Owczarek
+	New Results for Directed Vesicles and Chains near an Attractive Wall	1998	R Brak J W Essam A L Owczarek
+	On anisotropic spiral self-avoiding walks	1998	R Brak A L Owczarek C E Soteros
+ PDF Chat	On the hulls of directed percolation clusters	1997	A L Owczarek Andrew Rechnitzer R Brak A J Guttmann
+	Series expansion analysis of the backbone properties of two-dimensional percolation clusters	1997	F M Bhatti R Brak J W Essam Turab Lookman
+	New Monte Carlo algorithms for interacting self-avoiding walks	1997	Polidoros Paul Nidras R Brak
+	Low-temperature 2D polymer partition function scaling: series analysis results	1994	D Bennett-Wood R Brak A J Guttmann A L Owczarek Thomas Prellberg
+	Finite-length scaling of collapsing directed walks	1993	Thomas Prellberg A L Owczarek R Brak A J Guttmann
+	Directed animals on two-dimensional lattices	1993	Andrew Conway R Brak A J Guttmann
+	Exact solution of the staircase and row-convex polygon perimeter and area generating function	1990	R Brak A J Guttmann
+	Reciprocal relations for the weight factors arising in the series expansion of backbone percolation functions	1989	R Brak J W Essam M F Sykes
+	Absorption probability distribution for rough surfaces	1987	Michael Wilkinson R Brak
+	An exact solution for a spiral self-avoiding walk model on the triangular lattice	1985	G S Joyce R Brak
+	On the percolation threshold for a d-dimensional simple hypercubic lattice	1984	D S Gaunt R Brak

Common Coauthors

Coauthor	Papers Together
A L Owczarek	19
J W Essam	15
Andrew Rechnitzer	9
A J Guttmann	5
Thomas Prellberg	5
S G Whittington	5
G K Iliev	3
Mireille Bousquet‐Mélou	3
W. Frank Moore	2
Patrick Dyke	2
Amotz Oppenheim	2
Judy-anne H. Osborn	2
V. Rittenberg	1
D Bennett-Wood	1
F M Bhatti	1
M F Sykes	1
Turab Lookman	1
Michael Wilkinson	1
J. Lee	1
Polidoros Paul Nidras	1
Robert Parviainen	1
W. Galléas	1
Jan de Gier	1
G S Joyce	1
N. Mahony	1
C E Soteros	1
J Lee	1
D S Gaunt	1
Sylvie Corteel	1
H Lonsdale	1
Andrew Conway	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Binomial determinants, paths, and hook length formulae	1985	Ira M. Gessel Gérard Viennot	12
+	New Results for Directed Vesicles and Chains near an Attractive Wall	1998	R Brak J W Essam A L Owczarek	11
+ PDF Chat	Asymmetric exclusion model and weighted lattice paths	2004	R Brak J W Essam	8
+ PDF Chat	From the Bethe Ansatz to the Gessel-Viennot theorem	1999	R Brak J W Essam A L Owczarek	7
+	Vicious walkers and Young tableaux I: without walls	1998	A J Guttmann A L Owczarek Xavier Gérard Viennot	7
+	Return polynomials for non-intersecting paths above a surface on the directed square lattice	2001	R Brak J W Essam	7
+ PDF Chat	Exact solution of a 1D asymmetric exclusion model using a matrix formulation	1993	Bernard Derrida M. R. Evans Vincent Hakim Vincent Pasquier	7
+	Exact solution of<i>N</i>directed non-intersecting walks interacting with one or two boundaries	1999	R Brak J W Essam A L Owczarek	7
+	Probability of survival for vicious walkers near a cliff	1989	Peter J. Forrester	6
+	Combinatorial aspects of continued fractions	1980	Philippe Flajolet	6
+	Enumerative Combinatorics	1997	Richard P. Stanley Gian‐Carlo Rota	6
+	Combinatorial Problems Suggested by the Statistical Mechanics of Domains and of Rubber-Like Molecules	1956	H. N. V. Temperley	6
+	The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles	2015	E J Janse van Rensburg	5
+ PDF Chat	Relations between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for non-associative products	1948	Th. Motzkin	5
+	Algebraic languages and polyominoes enumeration	1984	M. Delest Gérard Viennot	5
+	On the number of certain lattice polygons	1969	Georg Pólya	5
+	Residual Entropy of Square Ice	1967	Élliott H. Lieb	4
+	Exact solution of the staircase and row-convex polygon perimeter and area generating function	1990	R Brak A J Guttmann	4
+ PDF Chat	A directed walk model of a long chain polymer in a slit with attractive walls	2005	R Brak A L Owczarek Andrew Rechnitzer S G Whittington	4
+	Lattice animals and heaps of dimers	2002	Mireille Bousquet‐Mélou Andrew Rechnitzer	4
+ PDF Chat	Partial difference equation method for lattice path problems	1999	R Brak J W Essam A L Owczarek	4
+	A combinatorial theory for general orthogonal polynomials with extensions and applications	1985	Gérard Viennot	4
+	Random self-avoiding walks on one-dimensional lattices	1990	ALM Sven Erick Svante Janson	4
+	A method for the enumeration of various classes of column-convex polygons	1996	Mireille Bousquet‐Mélou	4
+	Self-avoiding walks subject to boundary constraints	1977	Frederick T. Wall W. A. Seitz John C. Chin Frederic Mandel	3
+	Self-avoiding walks in wedges	1985	J. M. Hammersley S G Whittington	3
+ PDF Chat	Orthogonal Polynomials	1971		3
+	Heaps of pieces, I : Basic definitions and combinatorial lemmas	1986	Gérard Viennot	3
+	Exact solution of the discrete (1+1)-dimensional SOS model with field and surface interactions	1993	A L Owczarek Thomas Prellberg	3
+	An exact solution of a one-dimensional asymmetric exclusion model with open boundaries	1992	Bernard Derrida Eytan Domany David Mukamel	3
+ PDF Chat	Exact solution of a partially asymmetric exclusion model using a deformed oscillator algebra	2000	Richard A. Blythe M. R. Evans Francesca Colaiori Fabian H. L. Eßler	3
+ PDF Chat	One-dimensional partially asymmetric simple exclusion process with open boundaries: orthogonal polynomials approach	1999	Tomohiro Sasamoto	3
+	Equivalence of Cellular Automata to Ising Models and Directed Percolation	1984	Eytan Domany Wolfgang Kinzel	3
+ PDF Chat	Asymmetric simple exclusion process with open boundaries and Askey–Wilson polynomials	2004	Masaru Uchiyama Tomohiro Sasamoto Miki Wadati	3
+ PDF Chat	Phase transitions in an exactly soluble one-dimensional exclusion process	1993	G. Sch�tz Eytan Domany	3
+	Some q-analogues of the Schröder numbers arising from combinatorial statistics on lattice paths	1993	Joseph E. Bonin Louis W. Shapiro Rodica Simion	3
+	Exact solution of the lock step model of vicious walkers	1990	Peter J. Forrester	3
+ PDF Chat	The Asymmetric Exclusion Process and Brownian Excursions	2004	Bernard Derrida C. Enaud Joel L. Lebowitz	3
+ PDF Chat	Nonequilibrium steady states of matrix-product form: a solver's guide	2007	Richard A. Blythe M. R. Evans	3
+	Motzkin path models of long chain polymers in slits	2007	R Brak G K Iliev Andrew Rechnitzer S G Whittington	3
+	Asymptotic bounds for the number of convex n-ominoes	1974	David A. Klarner Ronald L. Rivest	3
+ PDF Chat	Walks in the quarter plane: Kreweras’ algebraic model	2005	Mireille Bousquet‐Mélou	2
+ PDF Chat	Directed Animals and Gas Models Revisited	2007	Yvan Le Borgne Jean‐François Marckert	2
+	Exact generating function for fully directed compact lattice animals	1988	Vladimir Privman N. M. Švrakić	2
+	Dyck path enumeration	1999	Emeric Deutsch	2
+ PDF Chat	Statistics of lattice animals (polyominoes) and polygons	2000	Iwan Jensen A J Guttmann	2
+	Generating functions for column-convex polyominoes	1988	M. Delest	2
+ PDF Chat	Nonequilibrium stationary states and equilibrium models with long range interactions	2004	R Brak Jan de Gier V. Rittenberg	2
+	Surface free energy of the critical six-vertex model with free boundaries	1989	A L Owczarek R. J. Baxter	2
+	Cluster structure near the percolation threshold	1982	Antonio Coniglio	2