Counting mobiles by integrable systems

التفاصيل البيبلوغرافية
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