02796nam 2200505 450 99646443950331620210316095213.03-030-67080-510.1007/978-3-030-67080-1(CKB)4100000011679114(DE-He213)978-3-030-67080-1(MiAaPQ)EBC6436020(PPN)252515668(EXLCZ)99410000001167911420210316d2021 uy 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierAn invitation to analytic combinatorics in several variables from one to several variables /Stephen Melczer1st ed. 2021.Cham, Switzerland :Springer,[2021]©20211 online resource (XVIII, 418 p. 45 illus., 36 illus. in color.) Texts and Monographs in Symbolic Computation3-030-67079-1 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 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.Texts and monographs in symbolic computation.Combinatorial analysisComputable functionsAlgorithmsCombinatorial analysis.Computable functions.Algorithms.511.6Melczer Stephen1074332MiAaPQMiAaPQMiAaPQBOOK996464439503316An invitation to analytic combinatorics in several variables2572399UNISA