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

详细信息	查看全文 | 推荐本文 |

• 作者：Sen-Peng Eu^a ; ^b ; ^{speu@nuk.edu.tw} ; Tung-Shan Fu^c ; ^{tsfu@npic.edu.tw} ; Yeh-Jong Pan^d ; ^{yjpan@mail.tajen.edu.tw} ; Chien-Tai Ting^a ; ^b ; ^{d0994101@mail.nuk.edu.tw} ; ^{chientaiting@gmail.com}
• 关键词：Sign-balance ; 321-avoiding permutation ; Alternating permutation ; Plane tree ; Dyck path ; Sign-reversing involution
• 刊名：Discrete Mathematics
• 出版年：2012
• 期刊代码：47_0012365x
• 类别：cp
• 出版时间：6 August, 2012
• 卷：312
• 期：15
• 页码：2228-2237
• 文件大小：335 K

摘要

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.