[seqfan] Re: 2 sequences from making triangles out of straws
Bruce Leenstra
maybeso83 at gmail.com
Thu Nov 24 22:32:39 CET 2016
Dear Neil,
I am also having trouble identifying similar triangles. Right at the start
with n=3 and same-color straws (3, 2, 3) is not listed - it is considered
the same triangle as (3, 3, 2). Then jumping to two color straws, the order
of colorings for same length sides is ignored - again treated as the same
triangle and coloring.
By this logic, with a symmetric triangle if you reverse the side order and
each coloring it will produce a duplicate triangle:
(3, 2', 2") (WWP, WW, PW) == (3, 2", 2') (PWW, WP, WW)
(3', 3", 2) (WWP, WPW, PW) == (3", 3', 2) (WPW, PWW, WP)
The consequence being - for each pair of triangles treated as the same
under some mapping, a pair of colorings must also be treated as the same
under the same mapping.
Regards, Bruce
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