[seqfan] A002996 - help re references "une probleme d'enumeration"

David Scambler dscambler at bmm.com
Fri Aug 24 10:11:48 CEST 2012


Can someone please assist with the following references in http://oeis.org/A002996 ?	

A. Errara, Analysis situs: une probleme d'enumeration, Memoires Acad. Bruxelles, Series 2, Vol. 11, No. 6, 26pp.
A. Errara, De quelques problemes d'analysis situs, Comptes Rend. Congr. Nat. Sci. Bruxelles, (1930), 106-110.

I counted the following:

Wrap a Dyck n-path around, rotate it until it returns to its original position, counting
each time the pattern matches the original un-rotated pattern.

The counts of n-paths with no such matches are 1, 1, 4, 12, 41, 126, 428 ... which is A002996.
And the count of n-paths with k additional matches is gives the same numbers aerated with k zeroes.

It is clear how and why the formula works, but I am curious about the original context of this sequence.

Any comments welcome.
Thanks
dave





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