@article{1a88e983847144709152023b4b560746,
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",
month = aug,
day = "6",
doi = "10.1016/j.disc.2012.03.024",
language = "English",
volume = "312",
pages = "2228--2237",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "15",
}