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Revision History for A359009

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Showing entries 1-10 | older changes
Irregular table read by rows: T(n,k) is the number of k-gons formed, k>=2, when every pair of n points, placed at the vertices of a regular n-gon, are connected by a circle and where the points lie at the ends of the circle's diameter.
(history; published version)
#23 by Michael De Vlieger at Tue Dec 13 10:14:15 EST 2022
STATUS

proposed

#22 by Scott R. Shannon at Tue Dec 13 07:14:18 EST 2022
STATUS

editing

#21 by Scott R. Shannon at Tue Dec 13 07:12:32 EST 2022
COMMENTS

Conjectures: for odd values of n all vertices are simple, other than those defining the diameters of the circles. For n > 2 and (n-2) mod 4 = 0, T(n,2) = n. For n mode 4 = 0, T(n,2) = k*n, k>=2. For odd n, T(n,2) = 0.

Discussion
Tue Dec 13
07:14
Scott R. Shannon: Submitting A358782, A358783, A358746, A359009 together.
#20 by Scott R. Shannon at Tue Dec 13 07:06:52 EST 2022
NAME

Irregular table read by rows: T(n,k) is the number of k-gons formed, k>=2, when every pair of n points, placed at the vertices of an n-gon, are connected by a circle and where the points lie at the ends of the circle's diameter.

#19 by Scott R. Shannon at Tue Dec 13 07:05:26 EST 2022
LINKS

#18 by Scott R. Shannon at Tue Dec 13 07:04:04 EST 2022
LINKS

#17 by Scott R. Shannon at Mon Dec 12 21:16:08 EST 2022
NAME

Irregular table read by rows: Kgons

#16 by Scott R. Shannon at Mon Dec 12 19:55:23 EST 2022
COMMENTS

Conjectures: for odd values of n all vertices are simple, other than those defining the diameters of the circles. For n > 2 and (n-2) mod 4 = 0, T(n,2) = n. For n mode 4 = 0, T(n,2) = k*n, k>=2.

#15 by Scott R. Shannon at Mon Dec 12 19:54:05 EST 2022
COMMENTS

Conjecture: for odd values of n all vertices are simple, other than those defining the diameters of the circles. No formula for n, or only the odd values of n, is currently know.

#14 by Scott R. Shannon at Mon Dec 12 07:15:59 EST 2022
KEYWORD

nonn,more,tabf,changed