Tree-like Tableaux

@article{Aval2013TreelikeT,
  title={Tree-like Tableaux},
  author={Jean-Christophe Aval and A. Boussicault and P. Nadeau},
  journal={Electron. J. Comb.},
  year={2013},
  volume={20},
  pages={P34}
}
  • Jean-Christophe Aval, A. Boussicault, P. Nadeau
  • Published 2013
  • Mathematics, Computer Science
  • Electron. J. Comb.
  • In this work we introduce and study tree-like tableaux, which are certain fillings of Ferrers diagrams in simple bijection with permutation tableaux and alternative tableaux. We exhibit an elementary insertion procedure on our tableaux which gives a clear proof that tableaux of size n are counted by n!, and which moreover respects most of the well-known statistics studied originally on alternative and permutation tableaux. Our insertion procedure allows to define in particular two simple new… CONTINUE READING
    48 Citations

    Figures and Topics from this paper

    Explore Further: Topics Discussed in This Paper

    Corners in Tree – Like Tableaux
    • PDF
    Corners in Tree-Like Tableaux
    • 6
    • PDF
    Refined Enumeration of Corners in Tree-like Tableaux
    • PDF
    Enumeration of Corners in Tree-like Tableaux
    • 4
    • Highly Influenced
    • PDF
    Dyck tableaux
    • 10
    • PDF
    Occupied corners in tree-like tableaux
    • 7
    • PDF
    EW-Tableaux, Le-Tableaux, Tree-Like Tableaux and the Abelian Sandpile Model
    • 6
    • Highly Influenced
    • PDF
    Crossings of signed permutations and $q$-Eulerian numbers of type $B$
    • 11
    • PDF
    On the distribution of parameters in random weighted staircase tableaux
    • 2
    • PDF
    Enumeration of Corners in Tree-like Tableaux and a Conjectural (a,b)-analogue
    • 2
    • Highly Influenced
    • PDF

    References

    SHOWING 1-10 OF 43 REFERENCES
    The structure of alternative tableaux
    • P. Nadeau
    • Mathematics, Computer Science
    • J. Comb. Theory, Ser. A
    • 2011
    • 40
    • PDF
    Permutation tableaux and permutation patterns
    • 103
    • PDF
    Combinatorics on permutation tableaux of type A and type B
    • 17
    • PDF
    Bijections for permutation tableaux
    • 55
    • PDF
    Crossings of signed permutations and $q$-Eulerian numbers of type $B$
    • 11
    • PDF
    Combinatorics of the permutation tableaux of type B
    • 4
    • Highly Influential
    • PDF
    On Some Properties of Permutation Tableaux
    • 46
    • PDF
    Combinatorics of non-ambiguous trees
    • 15
    • PDF
    Total positivity for cominuscule Grassmannians
    • 45
    • Highly Influential
    • PDF