|
|
LINKS
|
Ludovic Schwob, Table of n, a(n) for n = 3..500 (terms 3..100 from T. D. Noe).
S. W. Golomb and L. R. Welch, On the enumeration of polygons, Amer. Math. Monthly, 67 (1960), 349-353.
S. W. Golomb and L. R. Welch, On the enumeration of polygons, Amer. Math. Monthly, 67 (1960), 349-353. [Annotated scanned copy]
Samuel Herman and Eirini Poimenidou, Orbits of Hamiltonian Paths and Cycles in Complete Graphs, arXiv:1905.04785 [math.CO], 2019.
E. M. Palmer and R. W. Robinson, Enumeration under two representations of the wreath product, Acta Math., 131 (1973), 123-143.
R. C. Read, Letter to N. J. A. Sloane, Feb 04 1971 (gives initial terms of this sequence, except he has a(6)=7 instead of 12)
R. C. Read, Letter to N. J. A. Sloane, 1992
R. C. Read, Combinatorial problems in theory of music, Discrete Math. 167 (1997), 543-551.
N. J. A. Sloane, Illustration of initial terms [Annotated page from Golomb-Welch article]
Venta Terauds and J. Sumner, Circular genome rearrangement models: applying representation theory to evolutionary distance calculations, arXiv preprint arXiv:1712.00858 [q-bio.PE], 2017.
Venta Terauds and Jeremy Sumner, A new algebraic approach to genome rearrangement models, arXiv:2012.11665 [q-bio.PE], 2020.
|
|
|
EXAMPLE
|
Label the vertices of a regular n-gon 1,2,...,n.
For n=3,4,5 representatives for the polygons counted here are:
(1,2,3,1),
(1,2,3,4,1), (1,2,4,3,1),
(1,2,3,4,5,1), (1,2,3,5,4,1), (1,2,4,5,3,1), (1,3,5,2,4,1).
For n=6:
(1,2,3,4,5,6,1), (1,2,3,4,6,5,1), (1,2,3,5,6,4,1),
(1,2,3,6,5,4,1), (1,2,4,3,6,5,1), (1,2,4,6,3,5,1),
(1,2,4,6,5,3,1), (1,2,5,3,6,4,1), (1,2,5,4,6,3,1),
(1,2,5,6,3,4,1), (1,2,6,4,5,3,1), (1,3,5,2,6,4,1).
|
