Stammering tableaux

@article{JosuatVergs2017StammeringT,
  title={Stammering tableaux},
  author={Matthieu Josuat-Verg{\`e}s},
  journal={Discret. Math. Theor. Comput. Sci.},
  year={2017},
  volume={19}
}
The PASEP (Partially Asymmetric Simple Exclusion Process) is a probabilistic model of moving particles, which is of great interest in combinatorics, since it was realized that its partition function counts a certain kind of tableaux. These tableaux have several variants such as permutations tableaux, alternative tableaux, tree-like tableaux, Dyck tableaux, etc. We introduce in this context certain walks in Young’s lattice, that we call stammering tableaux (by analogy with oscillating tableaux… Expand
Expected Value of Statistics on Type-B Permutation Tableaux
Type-B permutation tableaux are combinatorial objects introduced by Lam and Williams that have an interesting connection with the partially asymmetric simple exclusion process (PASEP). In this paper,Expand
Gessel polynomials, rooks, and extended Linial arrangements
  • Vasu Tewari
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 2019
TLDR
The excedance statistic on permutations to maximal nonattacking rook placements on certain rectangular boards is generalized by decomposing them into boards of staircase shape, and a combinatorial interpretation of the number of bounded regions in extended Linial arrangements in the setting of labeled rooted plane k-ary trees is given. Expand

References

SHOWING 1-10 OF 22 REFERENCES
Tableaux combinatorics for the asymmetric exclusion process
TLDR
It is proved that in the long time limit, the probability that the PASEP is in a particular configuration @t is essentially the generating function for permutation tableaux of shape @l(@t) enumerated according to three statistics. Expand
Combinatorics of the Three-Parameter PASEP Partition Function
TLDR
This work considers a partially asymmetric exclusion process (PASEP) on a finite number of sites with open and directed boundary conditions and shows that this partition function is the generating function of permutations with respect to right-to-left minima, right- to-left maxima, ascents, and 31-2 patterns. Expand
Growth diagrams, and increasing and decreasing chains in fillings of Ferrers shapes
TLDR
The growth diagram construction of Fomin is used to show that its growth diagram bijections do in fact provide alternative proofs of the results by Backelin, West and Xin and by Bousquet-Melou and Steingrimsson on the enumeration of permutations and involutions with restricted patterns. Expand
Permutations selon leurs pics, creux, doubles montées et double descentes, nombres d'euler et nombres de Genocchi
TLDR
It is shown that the type of a permutation on n letters is caracterized by a map @c[n]->[n], and the number of possible types is the Catalan number. Expand
Generalized Robinson-Schensted-Knuth correspondence
The Robinson-Schensted-Knuth correspondence RSK associates with any permutation a pair of paths in a Young graph. The duality theorem for finite partially ordered sets associates with each such set aExpand
Crossings and nestings of matchings and partitions
We present results on the enumeration of crossings and nestings for matchings and set partitions. Using a bijection between partitions and vacillating tableaux, we show that if we fix the sets ofExpand
Tableaux combinatorics for the asymmetric exclusion process
The partially asymmetric exclusion process (PASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lat...
Rook numbers and the normal ordering problem
  • A. Varvak
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 2005
TLDR
A new proof of the rook factorization theorem is given to provide an explicit formula for the coefficients ci,j of a word w, which is the normal order coefficients of the element (D + U)n in the Weyl algebra. Expand
Enumerative Combinatorics: Volume 1
Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition ofExpand
Cylindric plane partitions, lambda determinant, commutators in semicircular systems. (Partitions planes cylindriques, lambda déterminants, les commutateurs dans l'algèbre engendrée par un système semi-circulaire)
TLDR
A multi-parameter generalization of the λ-determinant is proved, generalizing a recent result by di Francesco, and an alternative, elementary proof that the semicircular system is a factor is given. Expand
...
1
2
3
...