Counting peaks and valleys in k-colored Motzkin paths

نویسندگان

  • Aristidis Sapounakis
  • Panagiotis Tsikouras
چکیده

This paper deals with the enumeration of k-colored Motzkin paths with a fixed number of (left and right) peaks and valleys. Further enumeration results are obtained when peaks and valleys are counted at low and high level. Many well-known results for Dyck paths are obtained as special cases.

برای دانلود رایگان 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

The Goulden-Jackson cluster method for monoid networks and an application to lattice path enumeration

Given a nite or countably in nite set A, let A∗ be the set of all nite sequences of elements of A, including the empty sequence. We call A an alphabet, the elements of A letters, and the elements of A∗ words. By de ning an associative binary operation on two words by concatenating them, we see that A∗ is a monoid under the operation of concatenation, and we call A∗ the free monoid on A. The com...

متن کامل

Crossings and Nestings in Colored Set Partitions

Chen, Deng, Du, Stanley, and Yan introduced the notion of k-crossings and k-nestings for set partitions, and proved that the sizes of the largest k-crossings and k-nestings in the partitions of an n-set possess a symmetric joint distribution. This work considers a generalization of these results to set partitions whose arcs are labeled by an r-element set (which we call r-colored set partitions...

متن کامل

Matrix identities on weighted partial Motzkin paths

We give a combinatorial interpretation of a matrix identity on Catalan numbers and the sequence (1, 4, 4, 4, . . .) which has been derived by Shapiro, Woan and Getu by using Riordan arrays. By giving a bijection between weighted partial Motzkin paths with an elevation line and weighted free Motzkin paths, we find a matrix identity on the number of weighted Motzkin paths and the sequence (1, k, ...

متن کامل

Counting Lattice Paths via a New Cycle Lemma

Let α, β,m, n be positive integers. Fix a line L : y = αx + β, and a lattice point Q = (m,n) on L. It is well known that the number of lattice paths from the origin to Q which touches L only at Q is given by β m+ n “m+ n m ” . We extend the above formula in various ways, in particular, we consider the case when α and β are arbitrary positive reals. The key ingredient of our proof is a new varia...

متن کامل

Standard 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 کامل

ذخیره در منابع من


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

عنوان ژورنال:
  • Electr. J. Comb.

دوره 12  شماره 

صفحات  -

تاریخ انتشار 2005