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

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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The First Higher Stasheff–Tamari Orders are Quotients of the Higher Bruhat Orders. / Williams, N.J.
In: The Electronic Journal of Combinatorics , Vol. 30, No. 1, P1.29, 10.02.2023.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Williams, NJ 2023, 'The First Higher Stasheff–Tamari Orders are Quotients of the Higher Bruhat Orders', The Electronic Journal of Combinatorics , vol. 30, no. 1, P1.29. https://doi.org/10.37236/10877

APA

Williams, N. J. (2023). The First Higher Stasheff–Tamari Orders are Quotients of the Higher Bruhat Orders. The Electronic Journal of Combinatorics , 30(1), Article P1.29. https://doi.org/10.37236/10877

Vancouver

Williams NJ. The First Higher Stasheff–Tamari Orders are Quotients of the Higher Bruhat Orders. The Electronic Journal of Combinatorics . 2023 Feb 10;30(1):P1.29. doi: 10.37236/10877

Author

Williams, N.J. / The First Higher Stasheff–Tamari Orders are Quotients of the Higher Bruhat Orders. In: The Electronic Journal of Combinatorics . 2023 ; Vol. 30, No. 1.

Bibtex

@article{8e1f4a780fa74b8499a00a602942e326,
title = "The First Higher Stasheff–Tamari Orders are Quotients of the Higher Bruhat Orders",
abstract = "We prove the conjecture that the higher Tamari orders of Dimakis and M{\"u}ller-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. ",
author = "N.J. Williams",
year = "2023",
month = feb,
day = "10",
doi = "10.37236/10877",
language = "English",
volume = "30",
journal = "The Electronic Journal of Combinatorics ",
issn = "1077-8926",
publisher = "Electronic Journal of Combinatorics",
number = "1",

}

RIS

TY - JOUR

T1 - The First Higher Stasheff–Tamari Orders are Quotients of the Higher Bruhat Orders

AU - Williams, N.J.

PY - 2023/2/10

Y1 - 2023/2/10

N2 - 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.

AB - 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.

U2 - 10.37236/10877

DO - 10.37236/10877

M3 - Journal article

VL - 30

JO - The Electronic Journal of Combinatorics

JF - The Electronic Journal of Combinatorics

SN - 1077-8926

IS - 1

M1 - P1.29

ER -