Sign-balance identities of Adin-Roichman type on 321-avoiding alternating permutations

Sen Peng Eu; Tung Shan Fu; Yeh Jong Pan; Chien Tai Ting

doi:10.1016/j.disc.2012.03.024

Sign-balance identities of Adin-Roichman type on 321-avoiding alternating permutations

Sen Peng Eu, Tung Shan Fu, Yeh Jong Pan, Chien Tai Ting^*

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

Adin and Roichman proved a set of refined sign-balance identities on 321-avoiding permutations respecting the last descent of the permutations, which we call the identities of Adin-Roichman type. In this work, we construct a new involution on plane trees that proves refined sign-balance properties on 321-avoiding alternating permutations respecting the first and last entries of the permutations respectively and obtain two sets of identities of Adin-Roichman type.

Original language	English
Pages (from-to)	2228-2237
Number of pages	10
Journal	Discrete Mathematics
Volume	312
Issue number	15
DOIs	https://doi.org/10.1016/j.disc.2012.03.024
Publication status	Published - 2012 Aug 6
Externally published	Yes

Keywords

321-avoiding permutation
Alternating permutation
Dyck path
Plane tree
Sign-balance
Sign-reversing involution

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2012.03.024

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title = "Sign-balance identities of Adin-Roichman type on 321-avoiding alternating permutations",

abstract = "Adin and Roichman proved a set of refined sign-balance identities on 321-avoiding permutations respecting the last descent of the permutations, which we call the identities of Adin-Roichman type. In this work, we construct a new involution on plane trees that proves refined sign-balance properties on 321-avoiding alternating permutations respecting the first and last entries of the permutations respectively and obtain two sets of identities of Adin-Roichman type.",

keywords = "321-avoiding permutation, Alternating permutation, Dyck path, Plane tree, Sign-balance, Sign-reversing involution",

author = "Eu, {Sen Peng} and Fu, {Tung Shan} and Pan, {Yeh Jong} and Ting, {Chien Tai}",

note = "Funding Information: Research partially supported by NSC grants 98-2115-M-390-002 (S.-P. Eu), 99-2115-M-251-001 (T.-S. Fu), and 99-2115-M-127-001 (Y.-J. Pan).",

year = "2012",

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doi = "10.1016/j.disc.2012.03.024",

language = "English",

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T1 - Sign-balance identities of Adin-Roichman type on 321-avoiding alternating permutations

AU - Eu, Sen Peng

AU - Fu, Tung Shan

AU - Pan, Yeh Jong

AU - Ting, Chien Tai

N1 - Funding Information: Research partially supported by NSC grants 98-2115-M-390-002 (S.-P. Eu), 99-2115-M-251-001 (T.-S. Fu), and 99-2115-M-127-001 (Y.-J. Pan).

PY - 2012/8/6

Y1 - 2012/8/6

N2 - Adin and Roichman proved a set of refined sign-balance identities on 321-avoiding permutations respecting the last descent of the permutations, which we call the identities of Adin-Roichman type. In this work, we construct a new involution on plane trees that proves refined sign-balance properties on 321-avoiding alternating permutations respecting the first and last entries of the permutations respectively and obtain two sets of identities of Adin-Roichman type.

AB - Adin and Roichman proved a set of refined sign-balance identities on 321-avoiding permutations respecting the last descent of the permutations, which we call the identities of Adin-Roichman type. In this work, we construct a new involution on plane trees that proves refined sign-balance properties on 321-avoiding alternating permutations respecting the first and last entries of the permutations respectively and obtain two sets of identities of Adin-Roichman type.

KW - 321-avoiding permutation

KW - Alternating permutation

KW - Dyck path

KW - Plane tree

KW - Sign-balance

KW - Sign-reversing involution

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DO - 10.1016/j.disc.2012.03.024

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JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 15

ER -

Sign-balance identities of Adin-Roichman type on 321-avoiding alternating permutations

Abstract

Keywords

ASJC Scopus subject areas

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