"소모스 수열(Somos sequence)"의 두 판 사이의 차이
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| 10번째 줄: | 10번째 줄: | ||
* 소모스 8,9는 정수수열이 아니다 | * 소모스 8,9는 정수수열이 아니다 | ||
* 정수수열이 되는가의 문제 (integrality)<br> | * 정수수열이 되는가의 문제 (integrality)<br> | ||
| − | * 합동식을 생각할 때의 주기성 문제 (periodicity modulo n)<br> | + | * 합동식을 생각할 때의 주기성 문제 (periodicity modulo n) '''[Robinson1992]'''<br> |
| 55번째 줄: | 55번째 줄: | ||
* http://oeis.org/A006722<br> | * http://oeis.org/A006722<br> | ||
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| + | <h5 style="margin: 0px; line-height: 2em;">소모스-8 수열</h5> | ||
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| + | * <math>a_{n+6}a_{n} = a_{n+5} a_{n+1} +a_{n+4}a_{n+2}+ a_{n+3}^2</math><br> | ||
| 88번째 줄: | 96번째 줄: | ||
* http://www.cut-the-knot.org/arithmetic/algebra/SimpleSomosSequence.shtml | * http://www.cut-the-knot.org/arithmetic/algebra/SimpleSomosSequence.shtml | ||
* http://faculty.uml.edu/jpropp/somos.html | * http://faculty.uml.edu/jpropp/somos.html | ||
| − | * | + | * van der Poorten, Alfred J. 2004. Elliptic curves and continued fractions. math/0403225 (March 14). http://arxiv.org/abs/math/0403225. |
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| 130번째 줄: | 139번째 줄: | ||
* Hone, A. N. W. 2005. Elliptic Curves and Quadratic Recurrence Sequences. Bulletin of the London Mathematical Society 37, no. 2 (April 1): 161 -171. doi:[http://dx.doi.org/10.1112/S0024609304004163 10.1112/S0024609304004163]. | * Hone, A. N. W. 2005. Elliptic Curves and Quadratic Recurrence Sequences. Bulletin of the London Mathematical Society 37, no. 2 (April 1): 161 -171. doi:[http://dx.doi.org/10.1112/S0024609304004163 10.1112/S0024609304004163]. | ||
* Swart, Christine, and Andrew Hone. 2005. Integrality and the Laurent phenomenon for Somos 4 sequences. math/0508094 (August 4). http://arxiv.org/abs/math/0508094 | * Swart, Christine, and Andrew Hone. 2005. Integrality and the Laurent phenomenon for Somos 4 sequences. math/0508094 (August 4). http://arxiv.org/abs/math/0508094 | ||
| − | * R. M. Robinson, "Periodicity of Somos sequences", Proc. Amer. Math. Soc., 116 (1992), 613-619. | + | * '''[Robinson1992]'''R. M. Robinson, "Periodicity of Somos sequences", Proc. Amer. Math. Soc., 116 (1992), 613-619. doi:[http://dx.doi.org/10.1090/S0002-9939-1992-1140672-5 10.1090/S0002-9939-1992-1140672-5] |
* David Gale, Mathematical Entertainments: "The strange and surprising saga of the Somos sequences", Math. Intelligencer, 13(1) (1991), pp. 40-42. | * David Gale, Mathematical Entertainments: "The strange and surprising saga of the Somos sequences", Math. Intelligencer, 13(1) (1991), pp. 40-42. | ||
* http://www.jstor.org/action/doBasicSearch?Query= | * http://www.jstor.org/action/doBasicSearch?Query= | ||
2011년 2월 25일 (금) 05:27 판
이 항목의 스프링노트 원문주소
개요
- 소모스 4,5,6,7 은 정수수열
- 소모스 8,9는 정수수열이 아니다
- 정수수열이 되는가의 문제 (integrality)
- 합동식을 생각할 때의 주기성 문제 (periodicity modulo n) [Robinson1992]
소모스-4 수열
- \(a_{n+4}a_{n} = a_{n+3} a_{n+2} + a_{n+1}^2\)
- 1, 1, 1, 1, 2, 3, 7, 23, 59, 314, 1529, 8209, 83313, 620297, 7869898, 126742987, 1687054711, 47301104551, 1123424582771, 32606721084786
- RecurrenceTable[{a[n] a[n - 4] == a[n - 1] a[n - 3] + a[n - 2]^2, a[1] == 1, a[2] == 1, a[3] == 1, a[4] == 1}, a, {n, 20}]
소모스5- 수열
- \(a_{n+5}a_{n} = a_{n+4} a_{n+1} + a_{n+3} a_{n+2}\)
- 1, 1, 1, 1, 1, 2, 3, 5, 11, 37, 83, 274, 1217, 6161, 22833, 165713, 1249441, 9434290, 68570323, 1013908933
- RecurrenceTable[{a[n] a[5 + n] == a[2 + n] a[3 + n] + a[1 + n] a[4 + n], a[1] == 1, a[2] == 1, a[3] == 1, a[4] == 1, a[5] == 1}, a, {n, 20}]
소모스-6 수열
- \(a_{n+6}a_{n} = a_{n+5} a_{n+1} +a_{n+4}a_{n+2}+ a_{n+3}^2\)
- 1, 1, 1, 1, 1, 1, 3, 5, 9, 23, 75, 421, 1103, 5047, 41783, 281527, 2534423, 14161887, 232663909, 3988834875[2]
- RecurrenceTable[{a[n] a[n - 6] == a[n - 1] a[n - 5] + a[n - 2] a[n - 4] + a[n - 3]^2, a[1] == 1, a[2] == 1, a[3] == 1, a[4] == 1, a[5] == 1, a[6] == 1}, a, {n, 20}]
소모스-8 수열
- \(a_{n+6}a_{n} = a_{n+5} a_{n+1} +a_{n+4}a_{n+2}+ a_{n+3}^2\)
재미있는 사실
- Math Overflow http://mathoverflow.net/search?q=
- 네이버 지식인 http://kin.search.naver.com/search.naver?where=kin_qna&query=
역사
- http://www.google.com/search?hl=en&tbs=tl:1&q=
- Earliest Known Uses of Some of the Words of Mathematics
- Earliest Uses of Various Mathematical Symbols
- 수학사연표
메모
- http://www.cut-the-knot.org/arithmetic/algebra/SimpleSomosSequence.shtml
- http://faculty.uml.edu/jpropp/somos.html
- van der Poorten, Alfred J. 2004. Elliptic curves and continued fractions. math/0403225 (March 14). http://arxiv.org/abs/math/0403225.
관련된 항목들
수학용어번역
- 단어사전 http://www.google.com/dictionary?langpair=en%7Cko&q=
- 발음사전 http://www.forvo.com/search/
- 대한수학회 수학 학술 용어집
- 남·북한수학용어비교
- 대한수학회 수학용어한글화 게시판
사전 형태의 자료
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Somos_sequence
- http://www.proofwiki.org/wiki/
- http://www.wolframalpha.com/input/?i=
- The Online Encyclopaedia of Mathematics
- NIST Digital Library of Mathematical Functions
- The On-Line Encyclopedia of Integer Sequences
관련논문
- Hone, A. N. W. 2005. Elliptic Curves and Quadratic Recurrence Sequences. Bulletin of the London Mathematical Society 37, no. 2 (April 1): 161 -171. doi:10.1112/S0024609304004163.
- Swart, Christine, and Andrew Hone. 2005. Integrality and the Laurent phenomenon for Somos 4 sequences. math/0508094 (August 4). http://arxiv.org/abs/math/0508094
- [Robinson1992]R. M. Robinson, "Periodicity of Somos sequences", Proc. Amer. Math. Soc., 116 (1992), 613-619. doi:10.1090/S0002-9939-1992-1140672-5
- David Gale, Mathematical Entertainments: "The strange and surprising saga of the Somos sequences", Math. Intelligencer, 13(1) (1991), pp. 40-42.
- http://www.jstor.org/action/doBasicSearch?Query=
- http://www.ams.org/mathscinet
- http://dx.doi.org/10.1090/S0002-9939-1992-1140672-5
관련도서
- Gale, David. 1998. Tracking The Automatic Ant: And Other Mathematical Explorations. Springer, May 29.
- 도서내검색
- 도서검색
관련기사
- 네이버 뉴스 검색 (키워드 수정)