A Bijection Between 3-Motzkin Paths and Schröder Paths With No Peak at Odd Height
نویسندگان
چکیده
A new bijection between 3-Motzkin paths and Schröder paths with no peak at odd height is presented, together with numerous consequences involving related combinatorial structures such as 2-Motzkin paths, ordinary Motzkin paths and Dyck paths.
منابع مشابه
From (2, 3)-Motzkin Paths to Schröder Paths
In this paper, we provide a bijection between the set of restricted (2, 3)-Motzkin paths of length n and the set of Schröder paths of semilength n. Furthermore, we give a one-to-one correspondence between the set of (2, 3)-Motzkin paths of length n and the set of little Schröder paths of semilength n + 1. By applying the bijections, we get the enumerations of Schröder paths according to the sta...
متن کاملHilly poor noncrossing partitions and (2, 3)-Motzkin paths
A hilly poor noncrossing partition is a noncrossing partition with the properties : (1) each block has at most two elements, (2) in its linear representation, any isolated vertex is covered by some arc. This paper defines basic pairs as a combinatorial object and gives the number of hilly poor noncrossing partitions with n blocks, which is closely related to Maximal Davenport-Schinzel sequences...
متن کاملInverses of Motzkin and Schröder Paths
We suggest three applications for the inverses: For the inverse Motzkin matrix we look at Hankel determinants, and counting the paths inside a horizontal band, and for the inverse Schröder matrix we look at the paths inside the same band, but ending on the top side of the band.
متن کاملStandard Young tableaux and colored Motzkin paths
In this paper, we propose a notion of colored Motzkin paths and establish a bijection between the n-cell standard Young tableaux (SYT) of bounded height and the colored Motzkin paths of length n. This result not only gives a lattice path interpretation of the standard Young tableaux but also reveals an unexpected intrinsic relation between the set of SYTs with at most 2d+ 1 rows and the set of ...
متن کاملMotzkin Paths with Vertical Edges
This paper considers finite lattice paths formed from the set of step vectors {→, ↗,↘, ↑, and ↓} with the restriction that vertical steps (↑, ↓) can not be consecutive. We provide a recurrence relation for enumerating paths that terminate a horizontal distance n and vertical distance m from the starting point and apply the relation to paths which are restricted to the first quadrant and paths w...
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:
دوره شماره
صفحات -
تاریخ انتشار 2009