000 | 03460nam a22005655i 4500 | ||
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001 | 978-3-030-67080-1 | ||
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008 | 201222s2021 sz | s |||| 0|eng d | ||
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_a9783030670801 _9978-3-030-67080-1 |
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_a10.1007/978-3-030-67080-1 _2doi |
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_a511.1 _223 |
100 | 1 |
_aMelczer, Stephen. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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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. |
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300 |
_aXVIII, 418 p. 45 illus., 36 illus. in color. _bonline resource. |
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_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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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. |
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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 |
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