LEADER 02796nam 2200505 450 001 996464439503316 005 20210316095213.0 010 $a3-030-67080-5 024 7 $a10.1007/978-3-030-67080-1 035 $a(CKB)4100000011679114 035 $a(DE-He213)978-3-030-67080-1 035 $a(MiAaPQ)EBC6436020 035 $a(PPN)252515668 035 $a(EXLCZ)994100000011679114 100 $a20210316d2021 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 13$aAn invitation to analytic combinatorics in several variables $efrom one to several variables /$fStephen Melczer 205 $a1st ed. 2021. 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$dİ2021 215 $a1 online resource (XVIII, 418 p. 45 illus., 36 illus. in color.) 225 1 $aTexts and Monographs in Symbolic Computation 311 $a3-030-67079-1 327 $aIntroduction -- Background and Motivation -- Smooth ACSV and Applications -- Non-Smooth ACSV. 330 $aThis book uses new mathematical tools to examine broad computability and complexity questions in enumerative combinatorics, with applications to other areas of mathematics, theoretical computer science, and physics. A focus on effective algorithms leads to the development of computer algebra software of use to researchers in these domains. After a survey of current results and open problems on decidability in enumerative combinatorics, the text shows how the cutting edge of this research is the new domain of Analytic Combinatorics in Several Variables (ACSV). The remaining chapters of the text alternate between a pedagogical development of the theory, applications (including the resolution by this author of conjectures in lattice path enumeration which resisted several other approaches), and the development of algorithms. The final chapters in the text show, through examples and general theory, how results from stratified Morse theory can help refine some of these computability questions. Complementing the written presentation are over 50 worksheets for the SageMath and Maple computer algebra systems working through examples in the text. 410 0$aTexts and monographs in symbolic computation. 606 $aCombinatorial analysis 606 $aComputable functions 606 $aAlgorithms 615 0$aCombinatorial analysis. 615 0$aComputable functions. 615 0$aAlgorithms. 676 $a511.6 700 $aMelczer$b Stephen$01074332 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996464439503316 996 $aAn invitation to analytic combinatorics in several variables$92572399 997 $aUNISA