84320 20200909105806.0 doi 10.1007/s10801-018-0854-y sideral 109558 ART-2019-109558 eng Aramayona, J. Trees, homology, and automorphism groups of right-angled Artin groups 2019 Access copy available to the general public Unrestricted We study the homology of an explicit finite-index subgroup of the automorphism group of a partially commutative group, in the case when its defining graph is a tree. More concretely, we give a lower bound on the first Betti number of this subgroup, based on the number and degree of a certain type of vertices, which we call deep. We then use combinatorial methods to analyze the average value of this Betti number, in terms of the size of the defining tree. info:eu-repo/grantAgreement/ES/DGA/European Regional Development Funds info:eu-repo/grantAgreement/ES/MINECO/MTM2015-67781 info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 0.805 2019 MATHEMATICS 159 / 324 = 0.491 2019 Q2 T2 0.763 2019 Discrete Mathematics and Combinatorics 2019 Q2 Algebra and Number Theory 2019 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Fernández, J.L. Fernández, P. (orcid)0000-0001-9147-1745 Martínez-Pérez, C. Universidad de Zaragoza 2006 005 Universidad de Zaragoza Dpto. Matemáticas Área Algebra 50, 3 (2019), 293-315 J. algebr. comb. JOURNAL OF ALGEBRAIC COMBINATORICS 0925-9899 624721 http://zaguan.unizar.es/record/84320/files/texto_completo.pdf Postprint 6781 http://zaguan.unizar.es/record/84320/files/texto_completo.jpg?subformat=icon icon Postprint https://link.springer.com/article/10.1007%2Fs10801-018-0854-y (online 2018) Texto completo de la revista oai:zaguan.unizar.es:84320 articulos driver 2020-09-09-10:49:51 ARTICLE