تقرير
Fibonacci numbers, consecutive patterns, and inverse peaks
| العنوان: | Fibonacci numbers, consecutive patterns, and inverse peaks |
|---|---|
| المؤلفون: | Troyka, Justin M., Zhuang, Yan |
| المصدر: | Adv. in Appl. Math. 141: Article #102406, 19 pp., 2022 |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 05A05, 05A15, 05A19, 05E05, 11B39, 68Q45 |
| الوصف: | We give multiple proofs of two formulas concerning the enumeration of permutations avoiding a monotone consecutive pattern with a certain value for the inverse peak number or inverse left peak number statistic. The enumeration in both cases is given by a sequence related to Fibonacci numbers. We also show that there is exactly one permutation whose inverse peak number is zero among all permutations with any fixed descent composition, and we give a few elementary consequences of this fact. Our proofs involve generating functions, symmetric functions, regular expressions, and monomino-domino tilings. Comment: 17 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2109.14774 |
| رقم الأكسشن: | edsarx.2109.14774 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |