Lattice paths and generalized cluster complexes

Sen Peng Eu; Tung Shan Fu

doi:10.1016/j.jcta.2007.12.011

Lattice paths and generalized cluster complexes

Sen Peng Eu^*, Tung Shan Fu

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

In this paper we propose a variant of the generalized Schröder paths and generalized Delannoy paths by giving a restriction on the positions of certain steps. This generalization turns out to be reasonable, as attested by the connection with the faces of generalized cluster complexes of types A and B. As a result, we derive Krattenthaler's F-triangles for these two types by a combinatorial approach in terms of lattice paths.

Original language	English
Pages (from-to)	1183-1210
Number of pages	28
Journal	Journal of Combinatorial Theory. Series A
Volume	115
Issue number	7
DOIs	https://doi.org/10.1016/j.jcta.2007.12.011
Publication status	Published - 2008 Oct
Externally published	Yes

Keywords

Delannoy paths
Generalized cluster complex
Lattice paths
Schröder paths

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jcta.2007.12.011

Cite this

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title = "Lattice paths and generalized cluster complexes",

abstract = "In this paper we propose a variant of the generalized Schr{\"o}der paths and generalized Delannoy paths by giving a restriction on the positions of certain steps. This generalization turns out to be reasonable, as attested by the connection with the faces of generalized cluster complexes of types A and B. As a result, we derive Krattenthaler's F-triangles for these two types by a combinatorial approach in terms of lattice paths.",

keywords = "Delannoy paths, Generalized cluster complex, Lattice paths, Schr{\"o}der paths",

author = "Eu, {Sen Peng} and Fu, {Tung Shan}",

note = "Funding Information: E-mail addresses: [email protected] (S.-P. Eu), [email protected] (T.-S. Fu). 1 Partially supported by National Science Council (NSC), Taiwan, under grant 95-2115-M-390-006-MY3 and TJ & MY Foundation. 2 Partially supported by NSC under grant 95-2115-M-215-001-MY2.",

year = "2008",

month = oct,

doi = "10.1016/j.jcta.2007.12.011",

language = "English",

volume = "115",

pages = "1183--1210",

journal = "Journal of Combinatorial Theory. Series A",

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AU - Eu, Sen Peng

AU - Fu, Tung Shan

N1 - Funding Information: E-mail addresses: [email protected] (S.-P. Eu), [email protected] (T.-S. Fu). 1 Partially supported by National Science Council (NSC), Taiwan, under grant 95-2115-M-390-006-MY3 and TJ & MY Foundation. 2 Partially supported by NSC under grant 95-2115-M-215-001-MY2.

PY - 2008/10

Y1 - 2008/10

N2 - In this paper we propose a variant of the generalized Schröder paths and generalized Delannoy paths by giving a restriction on the positions of certain steps. This generalization turns out to be reasonable, as attested by the connection with the faces of generalized cluster complexes of types A and B. As a result, we derive Krattenthaler's F-triangles for these two types by a combinatorial approach in terms of lattice paths.

AB - In this paper we propose a variant of the generalized Schröder paths and generalized Delannoy paths by giving a restriction on the positions of certain steps. This generalization turns out to be reasonable, as attested by the connection with the faces of generalized cluster complexes of types A and B. As a result, we derive Krattenthaler's F-triangles for these two types by a combinatorial approach in terms of lattice paths.

KW - Delannoy paths

KW - Generalized cluster complex

KW - Lattice paths

KW - Schröder paths

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M3 - Article

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SP - 1183

EP - 1210

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 7

ER -

Lattice paths and generalized cluster complexes

Abstract

Keywords

ASJC Scopus subject areas

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