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http://hdl.handle.net/11320/17800Pełny rekord metadanych
| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Ziobro, Rafał | - |
| dc.date.accessioned | 2025-01-10T10:06:52Z | - |
| dc.date.available | 2025-01-10T10:06:52Z | - |
| dc.date.issued | 2024 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 32, Issue 1, Pages 235–245 | pl |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/17800 | - |
| dc.description.abstract | In this article we construct formally the Pascal’s triangle using Mizar proof assistant. Using the same techniques, we show some similar constructions based on integer sequences. We also prove Lucas’s theorem providing useful registrations of clusters to enable more automation in calculations. | pl |
| dc.language.iso | en | pl |
| dc.publisher | DeGruyter Open | pl |
| dc.rights | Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) | pl |
| dc.rights.uri | https://creativecommons.org/licenses/by-sa/3.0/ | pl |
| dc.subject | arithmetic triangle | pl |
| dc.subject | binomial coefficient | pl |
| dc.subject | Lucas theorem | pl |
| dc.title | Pascal’s Triangle and Lucas’s Theorem | pl |
| dc.type | Article | pl |
| dc.rights.holder | © 2024 The Author(s) | pl |
| dc.rights.holder | CC BY-SA 3.0 license | pl |
| dc.identifier.doi | 10.2478/forma-2024-0020 | - |
| dc.description.Affiliation | Department of Carbohydrate Technology and Cereal Processing, University of Agriculture, Kraków, Poland | pl |
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| dc.description.references | Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17. | pl |
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| dc.description.references | Chelsea Edmonds. Formalising combinatorial structures and proof techniques in Isabelle/HOL. Apollo – University of Cambridge Repository, 2023. doi:10.17863/CAM.1088. | pl |
| dc.description.references | Chelsea Edmonds. Lucas’s theorem. Archive of Formal Proofs, 2020. https://isa-afp.org/entries/Lucas_Theorem.html, Formal proof development. | pl |
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| dc.description.references | Artur Korniłowicz. Elementary number theory problems. Part IX. Formalized Mathematics, 31(1):161–169, 2023. doi:10.2478/forma-2023-0015. | pl |
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| dc.description.references | Adam Naumowicz. Dataset description: Formalization of elementary number theory in Mizar. In Christoph Benzmüller and Bruce R. Miller, editors, Intelligent Computer Mathematics – 13th International Conference, CICM 2020, Bertinoro, Italy, July 26–31, 2020, Proceedings, volume 12236 of Lecture Notes in Computer Science, pages 303–308. Springer, 2020. doi:10.1007/978-3-030-53518-6_22. | pl |
| dc.description.references | Karol Pąk. Prime representing polynomial with 10 unknowns. Formalized Mathematics, 30(4):255–279, 2022. doi:10.2478/forma-2022-0021. | pl |
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| dc.description.references | Antoni Smoluk. Statystyka w XXI wieku. Przyszłość statystyki. Didactics of Mathematics, 14(18):59–70, 2017. doi:10.15611/dm.2017.14.06. | pl |
| dc.identifier.eissn | 1898-9934 | - |
| dc.description.volume | 32 | pl |
| dc.description.issue | 1 | pl |
| dc.description.firstpage | 235 | pl |
| dc.description.lastpage | 245 | pl |
| dc.identifier.citation2 | Formalized Mathematics | pl |
| dc.identifier.orcid | 0000-0001-9681-4380 | - |
| Występuje w kolekcji(ach): | Formalized Mathematics, 2024, Volume 32, Issue 1 | |
Pliki w tej pozycji:
| Plik | Opis | Rozmiar | Format | |
|---|---|---|---|---|
| Pascals-Triangle-and-Lucass-Theorem.pdf | 283,08 kB | Adobe PDF | Otwórz |
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