Counting permutations by runs

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:142

Article

Zhuang, Yan¹ 

[1] Brandeis Univ, Dept Math, MS 050, Waltham, MA 02453 USA

关键词: Permutations;    Increasing runs;    Peaks;    Valleys;    Noncommutative symmetric functions;   

DOI  :  10.1016/j.jcta.2016.04.002

来源: Elsevier

【 摘 要 】

In his Ph.D. thesis, Ira Gessel proved a reciprocity formula for noncommutative symmetric functions which enables one to count words and permutations with restrictions on the lengths of their increasing runs. We generalize Gessel's theorem to allow for a much wider variety of restrictions on increasing run lengths, and use it to complete the enumeration of permutations with parity restrictions on peaks and valleys, and to give a systematic method for obtaining generating functions for permutation statistics that are expressible in terms of increasing runs. Our methods can also be used to obtain analogous results for alternating runs in permutations. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free