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\iteman{io-port 06081402}
\itemau{Shevelev, Vladimir}
\itemti{Number of permutations with prescribed up-down structure as a function of two variables.}
\itemso{Integers 12, No. 4, 529-569 (2012).}
\itemab
Summary: We consider the number of permutations with prescribed up-down structure as a function of two arguments: the number $n$ of elements and the introduced up-down index $k$ of a permutation. We consider sets of permutations for which $k$ is a fixed number and when $k$ is a function of $n$. In the first case the number of permutations is a polynomial in $n$, the degree of which is defined by $k$.
\itemrv{~}
\itemcc{}
\itemut{alternating permutations; Eulerian numbers; Niven's signature for permutations}
\itemli{doi:10.1515/integers-2011-0122}
\end