There are EXACTLY 1493804444499093354916284290188948031229880469556 Ways to Derange a Standard Deck of Cards (Ignoring Suits) [and Many Other Such Useful Facts]

DOI10.54550/ECA2021V1S3R17zbMath1499.05031arXiv2101.10147OpenAlexW3209046124MaRDI QIDQ5054900

Christoph Koutschan, Doron Zeilberger, Shalosh B. XIV Ekhad

Publication date: 12 December 2022

Published in: Enumerative Combinatorics and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.10147

zbMATH Keywords

Laguerre polynomialAlmkvist-Zeilberger algorithmholonomic recurrencemultiset derangement

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Exact enumeration problems, generating functions (05A15) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Uses Software

• OEIS
• DEtools

Cites Work

• The method of differentiating under the integral sign
• A holonomic systems approach to special functions identities
• Derangements and Laguerre polynomials
• Advanced applications of the holonomic systems approach
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