The enumeration of generalized Tamari intervals
نویسندگان
چکیده
منابع مشابه
Two bijections on Tamari Intervals
We use a recently introduced combinatorial object, the interval-poset, to describe two bijections on intervals of the Tamari lattice. Both bijections give a combinatorial proof of some previously known results. The first one is an inner bijection between Tamari intervals that exchanges the initial rise and lower contacts statistics. Those were introduced by Bousquet-Mélou, Fusy, and Préville-Ra...
متن کاملThe representation of the symmetric group on m-Tamari intervals
Anm-ballot path of size n is a path on the square grid consisting of north and east unit steps, starting at (0, 0), ending at (mn, n), and never going below the line {x = my}. The set of these paths can be equipped with a lattice structure, called the m-Tamari lattice and denoted by T (m) n , which generalizes the usual Tamari lattice Tn obtained when m = 1. This lattice was introduced by F. Be...
متن کاملThe Number of Intervals in the m-Tamari Lattices
MIREILLE BOUSQUET-MÉLOU, ÉRIC FUSY, AND LOUIS-FRANÇOIS PRÉVILLE-RATELLE Abstra t. An m-ballot path of size n is a path on the square grid onsisting of north and east steps, starting at (0, 0), ending at (mn, n), and never going below the line {x = my}. The set of these paths an be equipped with a latti e stru ture, alled the m-Tamari latti e and denoted by T (m) n , whi h generalizes the usual ...
متن کاملIntervals of balanced binary trees in the Tamari lattice
We show that the set of balanced binary trees is closed by interval in the Tamari lattice. We establish that the intervals [T, T ′] where T and T ′ are balanced binary trees are isomorphic as posets to a hypercube. We introduce synchronous grammars that allow to generate tree-like structures and obtain fixed-point functional equations to enumerate these. We also introduce imbalance tree pattern...
متن کاملFrom generalized Tamari intervals to non-separable planar maps (extended abstract)
Let v be a grid path made of north and east steps. The lattice TAM(v), based on all grid paths weakly above the grid path v sharing the same endpoints as v, was introduced by Préville-Ratelle and Viennot (2014) and corresponds to the usual Tamari lattice in the case v = (NE). They showed that TAM(v) is isomorphic to the dual of TAM(←−v ), where←−v is the reverse of v with N and E exchanged. Our...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2017
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2016.10.003