Abstract

Given a crystallographic reduced root system and an element γ of the lattice generated by the roots, we study the minimum number |γ|, called the length of γ , of roots needed to express γ as sum of roots. This number is related to the linear functionals presenting the convex hull of the roots. The map γ → |γ| turns out to be the upper integral part of a piecewise-linear function with linearity domains the cones over the facets of this convex hull. In order to show this relation, we investigate the integral closure of the monoid generated by the roots in a facet. We study also the positive length, i.e., the minimum number of positive roots needed to write an element, and we prove that the two notions of length coincide only for the types A and C.

Autore Pugliese

• Chirivi' Rocco

Tutti gli autori

• R. Chirivì

Titolo volume/Rivista

JOURNAL OF ALGEBRAIC COMBINATORICS

Anno di pubblicazione

2014

ISSN

0925-9899

ISBN

Non Disponibile

Numero di citazioni Wos

2

Ultimo Aggiornamento Citazioni

28/04/2018

Numero di citazioni Scopus

4

Ultimo Aggiornamento Citazioni

28/04/2018

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile