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The First Higher Stasheff–Tamari Orders are Quotients of the Higher Bruhat Orders

التفاصيل البيبلوغرافية
العنوان: The First Higher Stasheff–Tamari Orders are Quotients of the Higher Bruhat Orders
المؤلفون: Williams, NJ
بيانات النشر: Department of Pure Mathematics and Mathematical Statistics
//dx.doi.org/10.37236/10877
Electronic Journal of Combinatorics
The Electronic Journal of Combinatorics
سنة النشر: 2023
المجموعة: Apollo - University of Cambridge Repository
مصطلحات موضوعية: 4904 Pure Mathematics, 49 Mathematical Sciences
الوصف: We prove the conjecture that the higher Tamari orders of Dimakis and Müller-Hoissen coincide with the first higher Stasheff-Tamari orders. To this end, we show that the higher Tamari orders may be conceived as the image of an order-preserving map from the higher Bruhat orders to the first higher Stasheff-Tamari orders. This map is defined by taking the first cross-section of a cubillage of a cyclic zonotope. We provide a new proof that this map is surjective and show further that the map is full, which entails the aforementioned conjecture. We explain how order-preserving maps which are surjective and full correspond to quotients of posets. Our results connect the first higher Stasheff-Tamari orders with the literature on the role of the higher Tamari orders in integrable systems.
نوع الوثيقة: article in journal/newspaper
وصف الملف: application/pdf
اللغة: English
Relation: https://www.repository.cam.ac.uk/handle/1810/374669
الاتاحة: https://www.repository.cam.ac.uk/handle/1810/374669
Rights: Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0) ; https://creativecommons.org/licenses/by-nd/4.0/
رقم الانضمام: edsbas.CD7091BE
قاعدة البيانات: BASE
الوصف
الوصف غير متاح.