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Lattice Path Combinatorics and Applications

Part of the Developments in Mathematics Book Series (volume 58)

Editors: Andrews, George E.; Krattenthaler, Christian; Krinik, Alan

DOI: 10.1007/978-3-030-11102-1

ISBN: 978-3-030-11101-4

Publisher: Springer International Publishing - Springer Journals

Mar 3, 2019

1 - 10 of 17 Chapters

LitStream

Chapter 1Professor Lajos Takács: A Tribute

Haghighi, Aliakbar Montazer; Mohanty, Sri Gopal

Pages: 1 –28

[The paper consists of four parts. The first part is a description of the first author’s recollection of Takács - their acquaintance, him as a teacher and a mentor. In the second part, he recounts Takács’ life from his childhood to schools, university, employment and retirement, and his...
LitStream

Chapter 2The Distribution of the Local Time of Brownian Motion with Drift

Takács, Lajos

Pages: 29 –42

[In this paper Brownian motion with drift is considered, and explicit formulas are given for the distribution function, the density function, and the moments of the local time of the process and of the local time of the absolute value of the process.]
LitStream

Chapter 3Reflections on Shreeram Abhyankar

Alladi, Krishnaswami

Pages: 43 –46

[These are some reflections on the great algebraic geometer Shreeram Abhyankar given at the Banquet at the International Conference on Lattice Path Combinatorics and Applications, California Polytechnic University, Pomona, on Thursday, August 20, 2015.]
LitStream

Chapter 4My Association and Collaboration with George Andrews

Alladi, Krishnaswami

Pages: 47 –70

[These are personal reflections on my association, and a report of my collaboration, with George Andrews given at the International Conference on Lattice Path Combinatorics and Applications, California Polytechnic University, Pomona.]
LitStream

Chapter 5A Refinement of the Alladi–Schur Theorem

Andrews, George E.

Pages: 71 –77

[K. Alladi first observed a variant of I. Schur’s 1926 partition theorem. Namely, the number of partitions of n in which all parts are odd and none appears more than twice equals the number of partitions of n in which all parts differ by at least 3 and more than 3 if one of the parts is a...
LitStream

Chapter 6Explicit Formulas for Enumeration of Lattice Paths: Basketball and the Kernel Method

Banderier, Cyril; Krattenthaler, Christian; Krinik, Alan; Kruchinin, Dmitry; Kruchinin, Vladimir; Nguyen, David; Wallner, Michael

Pages: 78 –118

[This article deals with the enumeration of directed lattice walks on the integers with any finite set of steps, starting at a given altitude j and ending at a given altitude k, with additional constraints, for example, to never attain altitude 0 in-between. We first discuss the case of walks on...
LitStream

Chapter 7The Kernel Method for Lattice Paths Below a Line of Rational Slope

Banderier, Cyril; Wallner, Michael

Pages: 119 –154

[We analyze some enumerative and asymptotic properties of lattice paths below a line of rational slope. We illustrate our approach with Dyck paths under a line of slope 2 / 5. This answers Knuth’s problem #4 from his “Flajolet lecture” during the conference “Analysis of Algorithms” (AofA’2014) in...
LitStream

Chapter 8Enumeration of Colored Dyck Paths Via Partial Bell Polynomials

Birmajer, Daniel; Gil, Juan B.; McNamara, Peter R. W.; Weiner, Michael D.

Pages: 155 –165

[We consider a class of lattice paths with certain restrictions on their ascents and down-steps and use them as building blocks to construct various families of Dyck paths. We let every building block Pj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}...
LitStream

Chapter 9A Review of the Basic Discrete q-Distributions

Charalambides, Ch. A.

Pages: 166 –193

[Consider a sequence of independent Bernoulli trials and assume that the probability (or odds) of success (or the probability (or odds) of failure) at a trial varies (increases or decreases) geometrically, with rate q, either with the number of trials or with the number of successes. Let...
LitStream

Chapter 10Families of Parking Functions Counted by the Schröder and Baxter Numbers

Cori, Robert; Duchi, Enrica; Guerrini, Veronica; Rinaldi, Simone

Pages: 194 –225

[We define two new families of parking functions: one counted by Schröder numbers and the other by Baxter numbers. These families both include the well-known class of non-decreasing parking functions, which is counted by Catalan numbers and easily represented by Dyck paths, and they both are...

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