Dyck paths with coloured ascents
نویسندگان
چکیده
We introduce a notion of Dyck paths with coloured ascents. For several ways of colouring, we establish bijections between sets of such paths and other combinatorial structures, such as non-crossing trees, dissections of a convex polygon, etc. In some cases enumeration gives new expression for sequences enumerating these structures.
منابع مشابه
The Descent Statistic on 123-avoiding Permutations
We exploit Krattenthaler’s bijection between 123-avoiding permutations and Dyck paths to determine the Eulerian distribution over the set Sn(123) of 123-avoiding permutations in Sn. In particular, we show that the descents of a permutation correspond to valleys and triple ascents of the associated Dyck path. We get the Eulerian numbers of Sn(123) by studying the joint distribution of these two ...
متن کاملSome Combinatorics Related to Central Binomial Coefficients: Grand-Dyck Paths, Coloured Noncrossing Partitions and Signed Pattern Avoiding Permutations
We give some interpretations to certain integer sequences in terms of parameters on Grand-Dyck paths and coloured noncrossing partitions, and we find some new bijections relating Grand-Dyck paths and signed pattern avoiding permutations. Next we transfer a natural distributive lattice structure on Grand-Dyck paths to coloured noncrossing partitions and signed pattern avoiding permutations, thus...
متن کاملKazhdan-Lusztig Polynomials of Thagomizer Matroids
We introduce thagomizer matroids and compute the Kazhdan-Lusztig polynomial of a rank n+1 thagomizer matroid by showing that the coefficient of tk is equal to the number of Dyck paths of semilength n with k long ascents. We also give a conjecture for the Sn-equivariant Kazhdan-Lusztig polynomial of a thagomizer matroid.
متن کاملBicoloured Dyck Paths and the Contact Polynomial for n Non-Intersecting Paths in a Half-Plane Lattice
In this paper configurations of n non-intersecting lattice paths which begin and end on the line y = 0 and are excluded from the region below this line are considered. Such configurations are called Hankel n−paths and their contact polynomial is defined by ẐH 2r(n;κ) ≡ ∑r+1 c=1 |H (n) 2r (c)|κc where H (n) 2r (c) is the set of Hankel n-paths which make c intersections with the line y = 0 the lo...
متن کاملStatistics on Pattern-avoiding Permutations
This thesis concerns the enumeration of pattern-avoiding permutations with respect to certain statistics. Our first result is that the joint distribution of the pair of statistics ‘number of fixed points’ and ‘number of excedances’ is the same in 321-avoiding as in 132-avoiding permutations. This generalizes a recent result of Robertson, Saracino and Zeilberger, for which we also give another, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Eur. J. Comb.
دوره 29 شماره
صفحات -
تاریخ انتشار 2008