There are EXACTLY 1493804444499093354916284290188948031229880469556 Ways to Derange a Standard Deck of Cards (Ignoring Suits) [and Many Other Such Useful Facts]
| Autor: | Doron Zeilberger, Christoph Koutschan, Shalosh B. Ekhad |
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| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Symbolic Computation multiset derangement Computer science holonomic recurrence Symbolic Computation (cs.SC) almkvist-zeilberger algorithm Computer security computer.software_genre laguerre polynomial 33F10 05A15 33D45 68W30 Standard 52-card deck FOS: Mathematics QA1-939 Mathematics - Combinatorics Combinatorics (math.CO) computer Mathematics |
| Zdroj: | Enumerative Combinatorics and Applications, Vol 1, Iss 3, p Article S2R17 (2021) |
| ISSN: | 2710-2335 |
| DOI: | 10.54550/eca2021v1s3r17 |
| Popis: | In this memorial tribute to Joe Gillis, who taught us that Special Functions count, we show how the seminal Even-Gillis integral formula for the number of derangements of a multiset, in terms of Laguerre polynomials, can be used to efficiently compute not only the number of the title, but much harder ones, when it is interfaced with Wilf-Zeilberger algorithmic proof theory. Accompanied by a Maple package and output files that can be gotten from https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/multider.html |
| Databáze: | OpenAIRE |
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