Geodesic
Generalized Stirling permutations and forests: higher-order Eulerian and Ward numbers
J. Fernando Barbero G.1 ; Jesús Salas2 ; Eduardo J.S. Villaseñor2
1Instituto de Estructura de la Materia, CSIC
2Universidad Carlos III de Madrid
The electronic journal of combinatorics, Tome 22 (2015) no. 3
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We define a new family of generalized Stirling permutations that can be interpreted in terms of ordered trees and forests. We prove that the number of generalized Stirling permutations with a fixed number of ascents is given by a natural three-parameter generalization of the well-known Eulerian numbers. We give the generating function for this new class of numbers and, in the simplest cases, we find closed formulas for them and the corresponding row polynomials. By using a non-trivial involution our generalized Eulerian numbers can be mapped onto a family of generalized Ward numbers, forming a Riordan inverse pair, for which we also provide a combinatorial interpretation.
DOI : 10.37236/4814
Classification : 05A05, 05A15, 05C30
Mots-clés : generalized Stirling permutations, increasing trees and forests, generalized Eulerian numbers, generalized Ward numbers

J. Fernando Barbero G.  1   ; Jesús Salas  2   ; Eduardo J.S. Villaseñor  2

1 Instituto de Estructura de la Materia, CSIC
2 Universidad Carlos III de Madrid 
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     author = {J. Fernando Barbero G. and Jes\'us Salas and Eduardo J.S. Villase\~nor},
     title = {Generalized {Stirling} permutations and forests: higher-order {Eulerian} and {Ward} numbers},
     journal = {The electronic journal of combinatorics},
     year = {2015},
     volume = {22},
     number = {3},
     doi = {10.37236/4814},
     zbl = {1323.05003},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/4814/}
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J. Fernando Barbero G.; Jesús Salas; Eduardo J.S. Villaseñor. Generalized Stirling permutations and forests: higher-order Eulerian and Ward numbers. The electronic journal of combinatorics, Tome 22 (2015) no. 3. doi: 10.37236/4814

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