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HOW TO DECOMPOSE A PERMUTATION INTO A PAIR OF LABELED DYCK PATHS BY PLAYING A GAME
PERMUTATION LABELED DYCK PATHS PLAYING A GAME
2015/8/14
We give a bijection between permutations of 1, . . . , 2n and certain pairs of Dyck paths with labels on the down steps. The bijection arises from a game in which two players alternate selecting from ...
Noncrossing Linked Partitions and Large (3, 2)-Motzkin Paths
Noncrossing linked partition Schroder path large (3 2)-Motzkin path (3 2)-Motzkin path Schrö der number
2014/6/3
Noncrossing linked partitions arise in the study of certain transforms in free probability theory. We explore the connection between noncrossing linked partitions and (3, 2)-Motzkin paths, where a (3,...
Labeled Ballot Paths and the Springer Numbers
Springer number snake of type Bn labeled ballot path labeled Dyck path bijection
2014/6/3
The Springer numbers are defined in connection with the irreducible root system of type Bn and also arise as the generalized Euler and class numbers introduced by Shanks. Combinatorial interpretations...
We characterize the connected components of the subset CN∗ of H∞ formed by the products bh, where b is Carleson-Newman Blaschke product and h ∈ H∞ is an inver-tible function.
On harmonious colouring of line graph of central graph of paths
Central graph paths line graph and harmonious Colouring
2010/9/10
In this paper, we present some properties of the central graph C(Pn) of a path, and its line graph [ ( n )] L C P . We mainly have our discussion on the harmonious chromatic number of C(Pn) and the li...
Pairs of Noncrossing Free Dyck Paths and Noncrossing Partitions
Dyck path free Dyck path plane partition noncrossing partition vacillating tableau
2014/6/3
Using the bijection between partitions and vacillating tableaux, we establish a correspondence between pairs of noncrossing free Dyck paths of length 2n and noncrossing partitions of [2n + 1] with n +...
Identities from Weighted Motzkin Paths
Narayana number Catalan number Motzkin path Weighted Motzkin path Multiple Dyck path Bijection
2014/6/3
Based on a weighted version of the bijection between Dyck paths and 2-Motzkin paths, we find combinatorial interpretations of two identities related to the Narayana polynomials and the Catalan numbers...
Matrix Identities on Weighted Partial Motzkin Paths
Catalan number Schroder number Dyck path Motzkin path partial Motzkin path free Motzkin path weighted Motzkin path Riordan array
2014/6/3
We give a combinatorial interpretation of a matrix identity on Catalan numbers and the sequence (1, 4, 42, 43, ...) which has been derived by Shapiro, Woan and Getu by using Riordan arrays. By giving ...
Parity Reversing Involutions on Plane Trees and 2-Motzkin Paths
plane tree Dyck path 2-Motzkin path Catalan number involution
2014/6/3
The problem of counting plane trees with n edges and an even or an odd number of leaves was studied by Eu, Liu and Yeh, in connection with an identity on coloring nets due to Stanley. This identity wa...
Riordan paths are Motzkin paths without horizontal steps on the x-axis. We establish a correspondence between Riordan paths and -avoiding derangements. We also present a combinatorial proof of a recur...