ANISOTROPIC STEP, SURFACE CONTACT, AND AREA WEIGHTED DIRECTED WALKS ON THE TRIANGULAR LATTICE

DOI10.1142/S0217979202010087zbMath1073.82560MaRDI QIDQ5312033

A. C. Oppenheim, Richard Brak, Aleksander L. Owczarek

Publication date: 30 August 2005

Published in: International Journal of Modern Physics B (Search for Journal in Brave)

zbMATH Keywords

triangular latticeDirected lattice walksEnumerating Combinatorial Objects methodmarked area

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) (q)-calculus and related topics (05A30) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Applications of basic hypergeometric functions (33D90)

Related Items

Area-width scaling in generalised Motzkin paths

Cites Work

• Generalized Dyck paths
• The asymptotic behavior of a family of sequences
• Walks, walls, wetting, and melting
• Some \(q\)-analogues of the Schröder numbers arising from combinatorial statistics on lattice paths
• Enumeration of plane trees by branches and endpoints
• A Catalan triangle
• Exact solution of the discrete \((1+1)\)-dimensional SOS model with field and surface interactions
• Catalan, Motzkin, and Riordan numbers
• Moments of Dyck paths
• Dyck path enumeration
• Some combinatorial interpretations of \(q\)-analogs of Schröder numbers
• Riordan arrays and combinatorial sums
• A methodology for plane tree enumeration
• A combinatorial interpretation of the recurrence \(f_{n+1}=6f_n-f_{n-1}\)
• On the recurrence \(f_{m+1}=b_m f_m-f_{m-1}\) and applications
• On the enumeration and generation of generalized Dyck words
• New results for directed vesicles and chains near an attractive wall
• Area of Catalan paths
• Noncrossing partitions
• Weighted lattice paths
• Runs, Slides and Moments
• A Combinatorial Interpretation of a Catalan Numbers Identity
• The Strong Law of Small Numbers
• The Editor's Corner: n Coins in a Fountain
• Asymptotic Limits for a Two-Dimensional Recursion
• The Bricklayer Problem and the Strong Cycle Lemma
• On the Second Number of Plutarch
• Hipparchus, Plutarch, Schroder, and Hough
• The Catalan Numbers, the Lebesgue Integral, and 4 n-2
• A Combinatorial Interpretation of Ramanujan's Continued Fraction
• Note on a “Square” Functional Equation
• Relations between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for non-associative products
• On the Solution of Linear Difference Equations
• Motzkin numbers
• Motzkin numbers
• Scaling analysis for the adsorption transition in a watermelon network of \(n\) directed non-intersecting walks