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| Author | : T. V. Narayana |
| Publisher | : Heritage |
| Total Pages | : 120 |
| Release | : 1979-12 |
| Genre | : Mathematics |
| ISBN | : 9781487587284 |
Lattice path combinatorics has developed greatly as a branch of probability studies recently, and the need for new books on the subject is obvious. It treats several recent results and it offers a powerful new tool for studying many problems in mathematical statistics.
| Author | : Tadepalli Venkata Narayana |
| Publisher | : Toronto ; Buffalo : University of Toronto Press |
| Total Pages | : 128 |
| Release | : 1979 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Chunwei Song |
| Publisher | : CRC Press |
| Total Pages | : 120 |
| Release | : 2024-09-17 |
| Genre | : Mathematics |
| ISBN | : 1040123414 |
This book endeavors to deepen our understanding of lattice path combinatorics, explore key types of special sequences, elucidate their interconnections, and concurrently champion the author's interpretation of the “combinatorial spirit”. The author intends to give an up-to-date introduction to the theory of lattice path combinatorics, its relation to those special counting sequences important in modern combinatorial studies, such as the Catalan, Schröder, Motzkin, Delannoy numbers, and their generalized versions. Brief discussions of applications of lattice path combinatorics to symmetric functions and connections to the theory of tableaux are also included. Meanwhile, the author also presents an interpretation of the "combinatorial spirit" (i.e., "counting without counting", bijective proofs, and understanding combinatorics from combinatorial structures internally, and more), hoping to shape the development of contemporary combinatorics. Lattice Path Combinatorics and Special Counting Sequences: From an Enumerative Perspective will appeal to graduate students and advanced undergraduates studying combinatorics, discrete mathematics, or computer science.
| Author | : Cristina Bazgan |
| Publisher | : Springer Nature |
| Total Pages | : 538 |
| Release | : 2022-05-29 |
| Genre | : Computers |
| ISBN | : 3031066782 |
This book constitutes the refereed proceedings of the 33rd International Workshop on Combinatorial Algorithms, IWOCA 2022, which took place as a hybrid event in Trier, Germany, during June 7-9, 2022.The 35 papers presented in these proceedings were carefully reviewed and selected from 86 submissions. They deal with diverse topics related to combinatorial algorithms, such as algorithms and data structures; algorithmic and combinatorical aspects of cryptography and information security; algorithmic game theory and complexity of games; approximation algorithms; complexity theory; combinatorics and graph theory; combinatorial generation, enumeration and counting; combinatorial optimization; combinatorics of words; computational biology; computational geometry; decompositions and combinatorial designs; distributed and network algorithms; experimental combinatorics; fine-grained complexity; graph algorithms and modelling with graphs; graph drawing and graph labelling; network theory and temporal graphs; quantum computing and algorithms for quantum computers; online algorithms; parameterized and exact algorithms; probabilistic andrandomized algorithms; and streaming algorithms.
| Author | : N. Balakrishnan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 576 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461241405 |
Sri Gopal Mohanty has made pioneering contributions to lattice path counting and its applications to probability and statistics. This is clearly evident from his lifetime publications list and the numerous citations his publications have received over the past three decades. My association with him began in 1982 when I came to McMaster Univer sity. Since then, I have been associated with him on many different issues at professional as well as cultural levels; I have benefited greatly from him on both these grounds. I have enjoyed very much being his colleague in the statistics group here at McMaster University and also as his friend. While I admire him for his honesty, sincerity and dedication, I appreciate very much his kindness, modesty and broad-mindedness. Aside from our common interest in mathematics and statistics, we both have great love for Indian classical music and dance. We have spent numerous many different subjects associated with the Indian music and hours discussing dance. I still remember fondly the long drive (to Amherst, Massachusetts) I had a few years ago with him and his wife, Shantimayee, and all the hearty discussions we had during that journey. Combinatorics and applications of combinatorial methods in probability and statistics has become a very active and fertile area of research in the recent past.
| Author | : Richard Stanley |
| Publisher | : Cambridge University Press |
| Total Pages | : 801 |
| Release | : 2023-08-17 |
| Genre | : Mathematics |
| ISBN | : 1009262491 |
Revised second volume of the standard guide to enumerative combinatorics, including the theory of symmetric functions and 159 new exercises.
| Author | : Richard P. Stanley |
| Publisher | : Cambridge University Press |
| Total Pages | : 600 |
| Release | : 2001-06-04 |
| Genre | : Mathematics |
| ISBN | : 9780521789875 |
An introduction, suitable for beginning graduate students, showing connections to other areas of mathematics.
| Author | : Stephen Melczer |
| Publisher | : Springer Nature |
| Total Pages | : 418 |
| Release | : 2020-12-22 |
| Genre | : Mathematics |
| ISBN | : 3030670805 |
This book uses new mathematical tools to examine broad computability and complexity questions in enumerative combinatorics, with applications to other areas of mathematics, theoretical computer science, and physics. A focus on effective algorithms leads to the development of computer algebra software of use to researchers in these domains. After a survey of current results and open problems on decidability in enumerative combinatorics, the text shows how the cutting edge of this research is the new domain of Analytic Combinatorics in Several Variables (ACSV). The remaining chapters of the text alternate between a pedagogical development of the theory, applications (including the resolution by this author of conjectures in lattice path enumeration which resisted several other approaches), and the development of algorithms. The final chapters in the text show, through examples and general theory, how results from stratified Morse theory can help refine some of these computability questions. Complementing the written presentation are over 50 worksheets for the SageMath and Maple computer algebra systems working through examples in the text.
| Author | : Richard P. Stanley |
| Publisher | : Cambridge University Press |
| Total Pages | : 225 |
| Release | : 2015-03-26 |
| Genre | : Mathematics |
| ISBN | : 1316299589 |
Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book gives for the first time a comprehensive collection of their properties and applications to combinatorics, algebra, analysis, number theory, probability theory, geometry, topology, and other areas. Following an introduction to the basic properties of Catalan numbers, the book presents 214 different kinds of objects counted by them in the form of exercises with solutions. The reader can try solving the exercises or simply browse through them. Some 68 additional exercises with prescribed difficulty levels present various properties of Catalan numbers and related numbers, such as Fuss-Catalan numbers, Motzkin numbers, Schröder numbers, Narayana numbers, super Catalan numbers, q-Catalan numbers and (q,t)-Catalan numbers. The book ends with a history of Catalan numbers by Igor Pak and a glossary of key terms. Whether your interest in mathematics is recreation or research, you will find plenty of fascinating and stimulating facts here.
