Improving the Florentine algorithms: recovering algorithms for Motzkin and Schröder paths

نویسنده

  • Axel Bacher
چکیده

We present random sampling procedures for Motzkin and Schröder paths, following previous work on Dyck paths. Our algorithms follow the anticipated rejection method of the Florentine algorithms (Barcucci et al. 1994+), but introduce a recovery idea to greatly reduce the probability of rejection. They use an optimal amount of randomness and achieve a better time complexity than the Florentine algorithms.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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 کامل

# a 49 Integers 12 ( 2012 ) Inverses of Motzkin and Schröder Paths

The connection between weighted counts of Motzkin paths and moments of orthogonal polynomials is well known. We look at the inverse generating function of Motzkin paths with weighted horizontal steps, and relate it to Chebyshev polynomials of the second kind. The inverse can be used to express the number of paths ending at a certain height in terms of those ending at height 0. Paths of a more g...

متن کامل

A Bijection Between 3-Motzkin Paths and Schröder Paths With No Peak at Odd Height

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.

متن کامل

Inverses 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 کامل

Staircase Tilings and Lattice Paths

We define a combinatorial structure, a tiling of the staircase in the R plane, that will allow us, when restricted in different ways, to create direct bijections to Dyck paths of length 2n, Motzkin paths of lengths n and n−1, as well as Schröder paths and little Schröder paths of length n.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • CoRR

دوره abs/1802.06030  شماره 

صفحات  -

تاریخ انتشار 2018