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

2010년 11월 22일 (월) 21:13 판

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 \(d_0=1\), \(d_k=1\)

(*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
Plot[d[k, i], {i, 0, 2 k}]

Golden Fields: A Case for the Heptagon
- Peter Steinbach, Mathematics Magazine Vol. 70, No. 1 (Feb., 1997), pp. 22-31

@@ 8번째 줄: / 8번째 줄: @@
 #  (*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
-* [http://pythagoras0.springnote.com/pages/3719171 원분다항식(cyclotomic polynomial)]
-* character tables of finite groups
-* values of Lie group characters at elements of finite order
-*  matrix entries in the modular group representation coming from rational VOAs<br>
-** [[Kac-Peterson modular S-matrix]]
-* [[quantum dimensions|quantum dimension]] in RCFT
-* [[fusion rules and Verlinde formula]]
-* [http://pythagoras0.springnote.com/pages/3719171 Jones index of][[subfactors and Jones indices|subfactors]]
@@ 77번째 줄: / 61번째 줄: @@
 <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103);">articles</h5>
+* [http://www.jstor.org/stable/2691048 Golden Fields: A Case for the Heptagon]<br>
+** Peter Steinbach, Mathematics Magazine Vol. 70, No. 1 (Feb., 1997), pp. 22-31
 * [[2010년 books and articles|논문정 리]]