Sign-balance identities of Adin-Roichman type on 321-avoiding alternating permutations
نویسندگان
چکیده
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 thiswork,we construct a new involution onplane 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. © 2012 Elsevier B.V. All rights reserved.
منابع مشابه
Equidistribution and Sign-Balance on 321-Avoiding Permutations
Let Tn be the set of 321-avoiding permutations of order n. Two properties of Tn are proved: (1) The last descent and last index minus one statistics are equidistributed over Tn, and also over subsets of permutations whose inverse has an (almost) prescribed descent set. An analogous result holds for Dyck paths. (2) The sign-and-last-descent enumerators for T2n and T2n+1 are essentially equal to ...
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 312 شماره
صفحات -
تاریخ انتشار 2012