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The first higher Stasheff-Tamari orders are quotients of the higher Bruhat orders

Research output: Working paper › Preprint

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The first higher Stasheff-Tamari orders are quotients of the higher Bruhat orders. / Williams, Nicholas J.
2020.

Research output: Working paper › Preprint

Harvard

Williams, NJ 2020 'The first higher Stasheff-Tamari orders are quotients of the higher Bruhat orders'.

APA

Williams, N. J. (2020). The first higher Stasheff-Tamari orders are quotients of the higher Bruhat orders.

Vancouver

Williams NJ. The first higher Stasheff-Tamari orders are quotients of the higher Bruhat orders. 2020 Dec 18.

Author

Williams, Nicholas J. / The first higher Stasheff-Tamari orders are quotients of the higher Bruhat orders. 2020.

Bibtex

@techreport{21f816759ff64ab8b71d748d167037ee,
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\{"}uller-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. ",
keywords = "math.CO, Primary: 06A07, Secondary: 05B45",
author = "Williams, {Nicholas J.}",
note = "42 pages (1.35x line spacing), 7 figures. v2: added references and improved notation in final two sections, along with other minor changes. v3: edited paper to reflect discovery that surjectivity was already known; changed formatting",
year = "2020",
month = dec,
day = "18",
language = "English",
type = "WorkingPaper",

}

RIS

TY - UNPB

T1 - The first higher Stasheff-Tamari orders are quotients of the higher Bruhat orders

AU - Williams, Nicholas J.

N1 - 42 pages (1.35x line spacing), 7 figures. v2: added references and improved notation in final two sections, along with other minor changes. v3: edited paper to reflect discovery that surjectivity was already known; changed formatting

PY - 2020/12/18

Y1 - 2020/12/18

N2 - We prove the conjecture that the higher Tamari orders of Dimakis and M\"uller-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 M\"uller-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.

KW - math.CO

KW - Primary: 06A07, Secondary: 05B45

M3 - Preprint

BT - The first higher Stasheff-Tamari orders are quotients of the higher Bruhat orders

ER -