1,2

This idea is that minimal manifold like the minimal Pisot would behave very much like permutations in braiding tripartite graphs while adding only one edge to each linking cycle. The Characteristic Polynomial seems to be Pisot like on a radius 3 instead of one. This result suggests the conjecture that there may exist higher level Pisots by their graph partite-ness radius.

F. R. K. Chung and R. L. Graham, Erdos on Graphs, AK Peters Ltd., MA, 1998

Terr, David and Weisstein, Eric W. "Pisot Number." http://mathworld.wolfram.com/PisotNumber.html

Eric Weisstein's World of Mathematics, "Complete Graph." http://mathworld.wolfram.com/CompleteGraph.html

M(n,m)->9 X 9 as 9-3 X 3 blocks:3 K(3)'s linked by 6 Minimal Pisot 3 X 3's v(k+1)=M(n,m)*v(k) a(n) = v(k)(1)

M = {{0, 1, 1, 0, 1, 0, 0, 1, 0}, {1, 0, 1, 0, 0, 1, 0, 0, 1}, {1, 1, 0, 1, 1, 0, 1, 1, 0}, {0, 1, 0, 0, 1, 1, 0, 1, 0}, {0, 0, 1, 1, 0, 1, 0, 0, 1}, {1, 1, 0, 1, 1, 1, 1, 1, 0}, {0, 1, 0, 0, 1, 0, 0, 1, 1}, {0, 0, 1, 0, 0, 1, 1, 0, 1}, {1, 1, 0, 1, 1, 0, 1, 1, 0}}; v[1] = {1, 1, 1, 1, 1, 1, 1, 1, 1}; v[n_] := v[n] = M.v[n - 1]; a = Table[Floor[v[n][[1]]], {n, 1, 50}]

Cf. A120658.

Sequence in context: A011270 A081923 A020064 this_sequence A121584 A059227 A081103

Adjacent sequences: A123586 A123587 A123588 this_sequence A123590 A123591 A123592

nonn,uned

Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Nov 12 2006