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

[allouche at math.jussieu.fr]

Dear all

A quick search seems to reveal that two names occur for
(possibly) the same person:
A(lfred) Errara
A(lfred) Errera

May be this can help in looking for these papers
or for their contents?

In particular going to the Jahrbuch f"ur Math.
at http://www.emis.de/MATH/JFM/JFM.html
and typing "Errera" as name and "analysis" as
word of the title, one gets three entries
(including the two below) and a review on them.

best
jean-paul

David Scambler <dscambler at bmm.com> a écrit :

> 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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