A Combinatorial Proof of a Result on Generalized Lucas Polynomials
We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2. The initial values are 〈0〉 = 2; 〈1〉= s, respectively.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2016-09-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/dema.2016.49.issue-3/dema-2016-0022/dema-2016-0022.xml?format=INT |
| _version_ | 1818420532153942016 |
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| author | Laugier Alexandre Saikia Manjil P. |
| author_facet | Laugier Alexandre Saikia Manjil P. |
| author_sort | Laugier Alexandre |
| collection | DOAJ |
| description | We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2. The initial values are 〈0〉 = 2; 〈1〉= s, respectively. |
| first_indexed | 2024-12-14T12:55:57Z |
| format | Article |
| id | doaj.art-1ded2daa30804c3c9410961059736287 |
| institution | Directory Open Access Journal |
| issn | 0420-1213 2391-4661 |
| language | English |
| last_indexed | 2024-12-14T12:55:57Z |
| publishDate | 2016-09-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-1ded2daa30804c3c94109610597362872022-12-21T23:00:33ZengDe GruyterDemonstratio Mathematica0420-12132391-46612016-09-0149326627010.1515/dema-2016-0022dema-2016-0022A Combinatorial Proof of a Result on Generalized Lucas PolynomialsLaugier Alexandre0Saikia Manjil P.1LYCÉE TRISTAN CORBIÈRE, 16 RUE DE KERVÉGUEN - BP 17149 - 29671, MORLAIX CEDEX, FRANCEDIPLOMA STUDENT, MATHEMATICS GROUP THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS 11, STRADA COSTIERA TRIESTE, ITALYWe give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2. The initial values are 〈0〉 = 2; 〈1〉= s, respectively.http://www.degruyter.com/view/j/dema.2016.49.issue-3/dema-2016-0022/dema-2016-0022.xml?format=INTbinomial theoremFibonacci numberFibonomial coefficientLucas number q-analogueGeneralized Lucas Polynomials |
| spellingShingle | Laugier Alexandre Saikia Manjil P. A Combinatorial Proof of a Result on Generalized Lucas Polynomials Demonstratio Mathematica binomial theorem Fibonacci number Fibonomial coefficient Lucas number q-analogue Generalized Lucas Polynomials |
| title | A Combinatorial Proof of a Result on Generalized Lucas Polynomials |
| title_full | A Combinatorial Proof of a Result on Generalized Lucas Polynomials |
| title_fullStr | A Combinatorial Proof of a Result on Generalized Lucas Polynomials |
| title_full_unstemmed | A Combinatorial Proof of a Result on Generalized Lucas Polynomials |
| title_short | A Combinatorial Proof of a Result on Generalized Lucas Polynomials |
| title_sort | combinatorial proof of a result on generalized lucas polynomials |
| topic | binomial theorem Fibonacci number Fibonomial coefficient Lucas number q-analogue Generalized Lucas Polynomials |
| url | http://www.degruyter.com/view/j/dema.2016.49.issue-3/dema-2016-0022/dema-2016-0022.xml?format=INT |
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