Geodesic
Extensions of partial cyclic orders, Euler numbers and multidimensional boustrophedons
Sanjay Ramassamy1
1École normale supérieure de Lyon
The electronic journal of combinatorics, Tome 25 (2018) no. 1

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Zbl arXiv
We enumerate total cyclic orders on $\left\{x_1,\ldots,x_n\right\}$ where we prescribe the relative cyclic order of consecutive triples $(x_i,x_{i+1},x_{i+2})$, with indices taken modulo $n$. In some cases, the problem reduces to the enumeration of descent classes of permutations, which is done via the boustrophedon construction. In other cases, we solve the question by introducing multidimensional versions of the boustrophedon. In particular we find new interpretations for the Euler up/down numbers and the Entringer numbers.
DOI : 10.37236/7145
Classification : 06A07, 05A05
Mots-clés : Euler numbers, boustrophedon, cyclic orders

Sanjay Ramassamy  1

1 École normale supérieure de Lyon 
Sanjay Ramassamy. Extensions of partial cyclic orders, Euler numbers and multidimensional boustrophedons. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/7145
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