An Invitation to Analytic Combinatorics From One to Several Variables /
Melczer, Stephen.
An Invitation to Analytic Combinatorics From One to Several Variables / [electronic resource] : by Stephen Melczer. - 1st ed. 2021. - XVIII, 418 p. 45 illus., 36 illus. in color. online resource. - Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria, 2197-8409 . - Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria, .
Introduction -- Background and Motivation -- Smooth ACSV and Applications -- Non-Smooth ACSV.
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 theorycan 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.
9783030670801
10.1007/978-3-030-67080-1 doi
Discrete mathematics.
Computer science--Mathematics.
Mathematical physics.
Algorithms.
Discrete Mathematics.
Symbolic and Algebraic Manipulation.
Mathematical Methods in Physics.
Algorithms.
QA297.4
511.1
An Invitation to Analytic Combinatorics From One to Several Variables / [electronic resource] : by Stephen Melczer. - 1st ed. 2021. - XVIII, 418 p. 45 illus., 36 illus. in color. online resource. - Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria, 2197-8409 . - Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria, .
Introduction -- Background and Motivation -- Smooth ACSV and Applications -- Non-Smooth ACSV.
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 theorycan 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.
9783030670801
10.1007/978-3-030-67080-1 doi
Discrete mathematics.
Computer science--Mathematics.
Mathematical physics.
Algorithms.
Discrete Mathematics.
Symbolic and Algebraic Manipulation.
Mathematical Methods in Physics.
Algorithms.
QA297.4
511.1