The Eulerian numbers on restricted centrosymmetric permutations

We study the descent distribution over the set of centrosymmetric permutations that avoid the pattern of length 3. Our main tool in the most puzzling case, namely, $\tau=123$ and $n$ even, is a bijection that associates a Dyck prefix of length $2n$ to every centrosymmetric permutation in $S_{2n}$ that avoids 123.Comment: 17 pages, 6 figure

Combinatorial properties of the numbers of tableaux of bounded height

We introduce an infinite family of lower triangular matrices ¡(s), where °s n;i counts the standard Young tableaux on n cells and with at most s columns on a suitable subset of shapes. We show that the entries of these matrices satisfy a three-term row recurrence and we deduce recursive and asymptotic properties for the total number ¿s(n) of tableaux on n cells and with at most s columns

Combinatorial properties of the numbers of tableaux of bounded height

We introduce an infinite family of lower triangular matrices $\Gamma^{(s)}$, where $\gamma_{n,i}^s$ counts the standard Young tableaux on $n$ cells and with at most $s$ columns on a suitable subset of shapes. We show that the entries of these matrices satisfy a three-term row recurrence and we deduce recursive and asymptotic properties for the total number $\tau_s(n)$ of tableaux on $n$ cells and with at most $s$ columns.Comment: 11 pages, 1 figur

Two permutation classes enumerated by the central binomial coefficients

We define a map between the set of permutations that avoid either the four patterns $3214,3241,4213,4231$ or $3124,3142,4123,4132$, and the set of Dyck prefixes. This map, when restricted to either of the two classes, turns out to be a bijection that allows us to determine some notable features of these permutations, such as the distribution of the statistics "number of ascents", "number of left-to-right maxima", "first element", and "position of the maximum element"Comment: 26 pages, 3 figure