Order-preserving maps from a poset to a chain, the order polytope, and the Todd class of the associated toric variety.
type: Item
instance of: scholarly article
title: Order-preserving maps from a poset to a chain, the order polytope, and the Todd class of the associated toric variety.
zbMATH Open document ID: 1046.52010
DOI: 10.1016/S0195-6698(03)00091-X
author: Hugh Thomas
published in: European Journal of Combinatorics
publication date: 2003-11-16T00:00:00Z
review text: The paper is concerned with three objects: a finite poset \(Q\), its order polytope \(P\), and the toric variety \(X\) associated to the outer normal fan of \(P\). It is known that the number \(| [n+1]^Q| \) of order-preserving maps from \(Q\) to the chain of \(n+1\) elements is equal to the number of lattice points in the \(n\)-fold dilation of \(P\). The main result of the paper is a new formula for \(| [n+1]^Q| \), obtained from this equality by applying techniques for counting lattice points. This formula could also be obtained if one knew that a certain cycle represents the Todd class of \(X\). The author conjectures that this is always the case for toric varieties arising from posets, and he proves the conjecture under the assumption that \(Q\) is a chain.
reviewed by: Emanuela De Negri
Mathematics Subject Classification ID: 52B20
Mathematics Subject Classification ID: 06A07
Mathematics Subject Classification ID: 14M25
zbMATH DE Number: 2003947
zbMATH Keywords: posets
zbMATH Keywords: order polytopes
zbMATH Keywords: toric varieties
zbMATH Keywords: Todd class
MaRDI profile type: Publication
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full work available at URL: s0195-6698(03)00091-x
OpenAlex ID: W1967094823
description: scientific article; zbMATH DE number 2003947