[seqfan] a(1) in A242941
Felix FrÃ¶hlich
felix.froe at googlemail.com
Sun Nov 2 00:31:28 CET 2014
Hello sequence fans,
I thought about A242941 a bit and wondered whether a(1) is correct as
listed. a(1) is the number of uniform tessellations in one-dimensional
space, i.e. the line. A uniform tessellation is a tessellation that is
vertex-transitive and whose facets, tiles or cells are uniform polytopes.
In one dimension, there is only one polytope, namely a line segment bounded
by two points. So, in one dimension, if x-x denotes a line-segment (i.e. a
one dimensional polytope) with x denoting the vertices and - the bounded
'interior', then one possible uniform tessellation is
x-x-x-x-x-x-x-x-x-x-x-x.
If a(1) is correct, then this is the only possible uniform tessellation in
one dimension. However, what about a case like
x-x----x-x----x-x----x-x----x
Would that also count as a uniform tessellation? If so, then a(1) doesn't
seem to be correct, as then there would be infinitely many tessellations.
So is a(1) in A242941 correct?
Best,
Felix
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