تقرير
Counting mobiles by integrable systems
العنوان: | Counting mobiles by integrable systems |
---|---|
المؤلفون: | Bergère, Michel, Eynard, Bertrand, Guitter, Emmanuel, Oukassi, Soufiane |
سنة النشر: | 2023 |
المجموعة: | Mathematics Mathematical Physics |
مصطلحات موضوعية: | Mathematical Physics, Mathematics - Combinatorics |
الوصف: | Mobiles are a particular class of decorated plane trees which serve as codings for planar maps. Here we address the question of enumerating mobiles in their most general flavor, in correspondence with planar Eulerian (i.e., bicolored) maps. We show that the generating functions for such mobiles satisfy a number of recursive equations which lie in the field of integrable systems, leading us to explicit expressions for these generating functions as ratios of particular determinants. In particular we recover known results for mobiles associated with uncolored maps and prove some conjectured formulas for the generating functions of mobiles associated with $p$-constellations. Comment: 70 pages, 9 figures |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2312.08196 |
رقم الأكسشن: | edsarx.2312.08196 |
قاعدة البيانات: | arXiv |
الوصف غير متاح. |