Additive functions on trees

Piroska Lakatos. "Additive functions on trees." Colloquium Mathematicae 89.1 (2001): 135-145. <http://eudml.org/doc/283946>.

@article{PiroskaLakatos2001,
abstract = { The motivation for considering positive additive functions on trees was a characterization of extended Dynkin graphs (see I. Reiten [R]) and applications of additive functions in representation theory (see H. Lenzing and I. Reiten [LR] and T. Hübner [H]). We consider graphs equipped with integer-valued functions, i.e. valued graphs (see also [DR]). Methods are given for constructing additive functions on valued trees (in particular on Euclidean graphs) and for characterizing their structure. We introduce the concept of almost additive functions, which are additive on each vertex of a graph except one (called the exceptional vertex). On (valued) trees (with fixed exceptional vertex) the almost additive functions are unique up to rational multiples. For valued trees a necessary and sufficient condition is given for the existence of positive almost additive functions. },
author = {Piroska Lakatos},
journal = {Colloquium Mathematicae},
keywords = {Dynkin diagrams; almost additive functions; Coxeter transformations; Coxeter polynomials; valued trees},
language = {eng},
number = {1},
pages = {135-145},
title = {Additive functions on trees},
url = {http://eudml.org/doc/283946},
volume = {89},
year = {2001},
}

TY - JOUR
AU - Piroska Lakatos
TI - Additive functions on trees
JO - Colloquium Mathematicae
PY - 2001
VL - 89
IS - 1
SP - 135
EP - 145
AB - The motivation for considering positive additive functions on trees was a characterization of extended Dynkin graphs (see I. Reiten [R]) and applications of additive functions in representation theory (see H. Lenzing and I. Reiten [LR] and T. Hübner [H]). We consider graphs equipped with integer-valued functions, i.e. valued graphs (see also [DR]). Methods are given for constructing additive functions on valued trees (in particular on Euclidean graphs) and for characterizing their structure. We introduce the concept of almost additive functions, which are additive on each vertex of a graph except one (called the exceptional vertex). On (valued) trees (with fixed exceptional vertex) the almost additive functions are unique up to rational multiples. For valued trees a necessary and sufficient condition is given for the existence of positive almost additive functions.
LA - eng
KW - Dynkin diagrams; almost additive functions; Coxeter transformations; Coxeter polynomials; valued trees
UR - http://eudml.org/doc/283946
ER -