LEVELNESS OF ORDER POLYTOPES

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date

2020

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Department of Mathematics and Systems Analysis

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Language

en

Pages

20
1261-1280

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SIAM Journal on Discrete Mathematics, Volume 34, issue 2

Abstract

Since Stanley's [Discrete Comput. Geom., 1 (1986), pp. 9-23] introduction of order polytopes, their geometry has been widely used to examine (algebraic) properties of finite posets. In this paper, we follow this route to examine the levelness property of order polytopes, a property generalizing Gorensteinness. This property has been recently characterized by Miyazaki [J. Algebra, 480 (2017), pp. 215-236] for the case of order polytopes. We provide an alternative characterization using weighted digraphs. Using this characterization, we give a new infinite family of level posets and show that determining levelness is in co-NP. Moreover, we show how a necessary condition of levelness of [J. Algebra, 431 (2015), pp. 138-161] can be restated in terms of digraphs. We then turn to the more general family of alcoved polytopes. We give a characterization for levelness of alcoved polytopes using the Minkowski sum. Then we study several cases when the product of two polytopes is level. In particular, we provide an example where the product of two level polytopes is not level.

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Keywords

order polytopes, Bellman-Ford algorithm, posets, level algebras, alcoved polytopes, PROPERTY, RINGS

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DOI

10.1137/19M1292345

Citation

Haase, C, Kohl, F & Tsuchiya, A 2020, ' LEVELNESS OF ORDER POLYTOPES ', SIAM Journal on Discrete Mathematics, vol. 34, no. 2, pp. 1261-1280 . https://doi.org/10.1137/19M1292345

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https://urn.fi/URN:NBN:fi:aalto-202009045292

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[article-cris] Perustieteiden korkeakoulu / SCI