[seqfan] Need help naming another "regular n-gon with all diagonals" sequence

chris_scussel at icloud.com chris_scussel at icloud.com
Mon Sep 25 02:38:56 CEST 2023

Greetings Seqfans,

    Recently I have corrected and extended A187781 (counting noncongruent regions)
and created A363979 (counting nonsimilar regions), both for "regular n-gons with all
diagonals". I am working on a related new sequence (currently unnumbered) that
I am having trouble describing succinctly.

    The concept is quite simple: the number of families of congruent regions,
where congruence follows directly from dihedral symmetries of the n-gon. This sequence
is the same as A187781 until n=12, at which point a "sporadic" congruence
(i.e., one not caused by dihedral symmetries) occurs. For n>12 such congruences
become more frequent and numerous.

    Among the potential descriptions I've considered are the following:       

A wordy description:

        The number of equivalence classes in an equivalence relation on the regions,
        where two regions are equivalent iff they map into each other via dihedral
        symmetries of the n-gon

One less wordy but also less to the point (and possibly not even correct):

        The maximum number of colors with which the regions can be colored while
        retaining all of the dihedral symmetries of the n-gon.

Neither of these include the necessary phrase "regular n-gon with all diagonals",
which would make them even longer.

I would appreciate any suggestions.

Thanks and Regards,


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