"Cyclotomic numbers and Chebyshev polynomials"의 두 판 사이의 차이

수학노트
둘러보기로 가기 검색하러 가기
(피타고라스님이 이 페이지의 이름을 cyclotomic numbers and Chebyshev polynomials로 바꾸었습니다.)
1번째 줄: 1번째 줄:
 +
<h5>introduction</h5>
  
 +
* borrowed from [[Andrews-Gordon identity]]
 +
*  quantum dimension and there recurrence relation<br><math>d_i=\frac{\sin \frac{(i+1)\pi}{k+2}}{\sin \frac{\pi}{k+2}}}</math> satisfies<br><math>d_i^2=1+d_{i-1}d_{i+1}</math> where <math>d_0=1</math>, <math>d_k=1</math><br>
 +
 +
 
 +
 +
#  (*choose k for c (2,k+2) minimal model*)k := 11<br> d[k_, i_] := Sin[(i + 1) Pi/(k + 2)]/Sin[Pi/(k + 2)]<br> Table[{i, d[k, i]}, {i, 1, k}] // TableForm<br> Table[{i, N[(d[k, i])^2 - (1 + d[k, i - 1]*d[k, i + 1]), 10]}, {i, 1,<br>    k}] // TableForm<br>
 +
#  Plot[d[k, i], {i, 0, 2 k}]<br>
 +
 +
 
 +
 +
 
 +
 +
<h5>cyclotomic numbers</h5>
 +
 +
* Gauss sums
 +
* character tables of finite groups
 +
* values of Lie group characters at elements of finite order
 +
* quantum dimensions in RCFT
 +
* matrix entries in the modular group representation coming from rational VOAs
 +
* index of subfactors ?
 +
 +
 
 +
 +
 
 +
 +
<h5>chebyshev polynomials</h5>
 +
 +
* [http://pythagoras0.springnote.com/pages/4682477 체비셰프 다항식]
 +
* http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html<br> also obey the interesting [http://mathworld.wolfram.com/Determinant.html determinant] identity<br><br>
 +
 +
 
 +
 +
 
 +
 +
<h5>history</h5>
 +
 +
* http://www.google.com/search?hl=en&tbs=tl:1&q=
 +
 +
 
 +
 +
 
 +
 +
<h5>related items</h5>
 +
 +
 
 +
 +
 
 +
 +
<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103);">encyclopedia</h5>
 +
 +
* http://ko.wikipedia.org/wiki/
 +
* http://en.wikipedia.org/wiki/
 +
* Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]])
 +
 +
 
 +
 +
 
 +
 +
<h5>books</h5>
 +
 +
 
 +
 +
* [[2010년 books and articles]]<br>
 +
* http://gigapedia.info/1/
 +
* http://gigapedia.info/1/
 +
* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
 +
 +
 
 +
 +
 
 +
 +
<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103);">articles</h5>
 +
 +
 
 +
 +
* [[2010년 books and articles|논문정 리]]
 +
* http://www.ams.org/mathscinet
 +
* http://www.zentralblatt-math.org/zmath/en/
 +
* http://pythagoras0.springnote.com/
 +
* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html]
 +
* http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
 +
* http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
 +
* http://dx.doi.org/
 +
 +
 
 +
 +
 
 +
 +
<h5>question and answers(Math Overflow)</h5>
 +
 +
* http://mathoverflow.net/search?q=
 +
* http://mathoverflow.net/search?q=
 +
 +
 
 +
 +
 
 +
 +
<h5>blogs</h5>
 +
 +
*  구글 블로그 검색<br>
 +
** http://blogsearch.google.com/blogsearch?q=
 +
** http://blogsearch.google.com/blogsearch?q=
 +
 +
 
 +
 +
 
 +
 +
<h5>experts on the field</h5>
 +
 +
* http://arxiv.org/
 +
 +
 
 +
 +
 
 +
 +
<h5>links</h5>
 +
 +
* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier]
 +
* [http://pythagoras0.springnote.com/pages/1947378 수식표 현 안내]
 +
* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]

2010년 3월 26일 (금) 10:20 판

introduction
  • borrowed from Andrews-Gordon identity
  • quantum dimension and there recurrence relation
    \(d_i=\frac{\sin \frac{(i+1)\pi}{k+2}}{\sin \frac{\pi}{k+2}}}\) satisfies
    \(d_i^2=1+d_{i-1}d_{i+1}\) where \(d_0=1\), \(d_k=1\)

 

  1. (*choose k for c (2,k+2) minimal model*)k := 11
    d[k_, i_] := Sin[(i + 1) Pi/(k + 2)]/Sin[Pi/(k + 2)]
    Table[{i, d[k, i]}, {i, 1, k}] // TableForm
    Table[{i, N[(d[k, i])^2 - (1 + d[k, i - 1]*d[k, i + 1]), 10]}, {i, 1,
       k}] // TableForm
  2. Plot[d[k, i], {i, 0, 2 k}]

 

 

cyclotomic numbers
  • Gauss sums
  • character tables of finite groups
  • values of Lie group characters at elements of finite order
  • quantum dimensions in RCFT
  • matrix entries in the modular group representation coming from rational VOAs
  • index of subfactors ?

 

 

chebyshev polynomials

 

 

history

 

 

related items

 

 

encyclopedia

 

 

books

 

 

 

articles

 

 

 

question and answers(Math Overflow)

 

 

blogs

 

 

experts on the field

 

 

links
원본 주소 "https://wiki.mathnt.net/index.php?title=Cyclotomic_numbers_and_Chebyshev_polynomials&oldid=33801"