Lattice Path Combinatorics and Applications

• Corporate Author: SpringerLink (Online service)
• Other Authors: Andrews, George E. (Editor, http://id.loc.gov/vocabulary/relators/edt), Krattenthaler, Christian (Editor, http://id.loc.gov/vocabulary/relators/edt), Krinik, Alan (Editor, http://id.loc.gov/vocabulary/relators/edt)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Developments in Mathematics, 58
• Subjects: Combinatorics.; Number theory.; Graph theory.; Convex geometry .; Discrete geometry.; Probabilities.; Number Theory.; Graph Theory.; Convex and Discrete Geometry.; Probability Theory and Stochastic Processes.

Recent methods used in lattice path combinatorics and various related branches of enumerative combinatorics are grouped together and presented in this volume, together with relevant applications. Contributions are mainly comprised of research articles though an attractive bonus is the inclusion of s...

Table of Contents:

• Preface
• Lajos Takács: A Tribute (A.M. Haghighi, S.G. Mohanty)
• The Distribution of the Local Time of Brownian Motion with Drift (L. Takács)
• Reflections on Shreeram Abhyankar (K. Alladi)
• My Association and Collaboration with George Andrews (K. Alladi)
• A Refinement of the Alladi-Schur Theorem (G.E. Andrews)
• Explicit Formulas for Enumeration of Lattice Paths: Basketball and the Kernel Method (C. Banderier, C. Krattenthaler, A. Krinik, D. Kruchinin, V. Kruchinin, D. Nguyen, M. Wallner)
• The Kernel Method for Lattice Paths below a Line of Rational Slope (C. Banderier, M. Wallner)
• Enumeration of Colored Dyck Paths via Partial Bell Polynomials (D. Birmajer, J.B. Gil, P.R.W. McNamara, M.D. Weiner)
• A Review of the Basic Discrete q-Distributions (Ch.A. Charalambides)
• Families of Parking Functions Counted by the Schröder and Baxter Numbers (R. Cori, E. Duchi, S. Rinaldi, V. Guerrini)
• Some Tilings, Colorings and Lattice Paths via Stern Polynomials (K. Dilcher, L. Ericksen)
• p-Rook Numbers and Cycle Counting in Cp|Sn (J. Haglund, J. Remmel, M. Yoo)
• Asymptotic Behaviour of Certain q-Poisson, q-Binomial and Negative q-Binomial Distributions (A. Kyriakoussis, M. Vamvakari)
• Asymptotic Estimates for Queueing Systems with Time-Varying Periodic Transition Rates (B. Margolius)
• A Combinatorial Analysis of the M/M[m]/1 Queue (G. Mercankosk, G.M. Nair)
• Laws Relating Runs, Long Runs, and Steps in Gambler's Ruin, with Persistence in Two Strata (G.J. Morrow)
• Paired Patterns in Lattice Paths (R.Pan, J.B. Remmel).