Projects per year
Abstract
Since Stanley's [Discrete Comput. Geom., 1 (1986), pp. 923] 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. 215236] 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 coNP. Moreover, we show how a necessary condition of levelness of [J. Algebra, 431 (2015), pp. 138161] 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.
Original language  English 

Pages (fromto)  12611280 
Number of pages  20 
Journal  SIAM Journal on Discrete Mathematics 
Volume  34 
Issue number  2 
DOIs  
Publication status  Published  2020 
MoE publication type  A1 Journal articlerefereed 
Keywords
 order polytopes
 BellmanFord algorithm
 posets
 level algebras
 alcoved polytopes
 PROPERTY
 RINGS
Projects

Lattice Polytopes in Algebra, Combinatorics, and Mathematical Physics
01/09/2019 → 31/08/2022
Project: Academy of Finland: Other research funding

Algebraic structures and random geometry of stochastic lattice models
Kytölä, K., Webb, C., Karrila, A., Radnell, D., Gutiérrez, A. W., Kohl, F., Orlich, M. & Abuzaid, O.
01/09/2015 → 31/08/2019
Project: Academy of Finland: Other research funding