000 03460nam a22005655i 4500
001 978-3-030-67080-1
003 DE-He213
005 20240423125348.0
007 cr nn 008mamaa
008 201222s2021 sz | s |||| 0|eng d
020 _a9783030670801
_9978-3-030-67080-1
024 7 _a10.1007/978-3-030-67080-1
_2doi
050 4 _aQA297.4
072 7 _aPBD
_2bicssc
072 7 _aMAT008000
_2bisacsh
072 7 _aPBD
_2thema
082 0 4 _a511.1
_223
100 1 _aMelczer, Stephen.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 3 _aAn Invitation to Analytic Combinatorics
_h[electronic resource] :
_bFrom One to Several Variables /
_cby Stephen Melczer.
250 _a1st ed. 2021.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2021.
300 _aXVIII, 418 p. 45 illus., 36 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aTexts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria,
_x2197-8409
505 0 _aIntroduction -- Background and Motivation -- Smooth ACSV and Applications -- Non-Smooth ACSV.
520 _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 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.
650 0 _aDiscrete mathematics.
650 0 _aComputer science
_xMathematics.
650 0 _aMathematical physics.
650 0 _aAlgorithms.
650 1 4 _aDiscrete Mathematics.
650 2 4 _aSymbolic and Algebraic Manipulation.
650 2 4 _aMathematical Methods in Physics.
650 2 4 _aAlgorithms.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783030670795
776 0 8 _iPrinted edition:
_z9783030670818
776 0 8 _iPrinted edition:
_z9783030670825
830 0 _aTexts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria,
_x2197-8409
856 4 0 _uhttps://doi.org/10.1007/978-3-030-67080-1
912 _aZDB-2-SCS
912 _aZDB-2-SXCS
942 _cSPRINGER
999 _c177114
_d177114