25 research outputs found
The planar Cayley graphs are effectively enumerable I: consistently planar graphs
We obtain an effective enumeration of the family of finitely generated groups
admitting a faithful, properly discontinuous action on some 2-manifold
contained in the sphere. This is achieved by introducing a type of group
presentation capturing exactly these groups.
Extending this in a companion paper, we find group presentations capturing
the planar finitely generated Cayley graphs. Thus we obtain an effective
enumeration of these Cayley graphs, yielding in particular an affirmative
answer to a question of Droms et al.Comment: To appear in Combinatorica. The second half of the previous version
is arXiv:1901.0034
Researches of semigroups with planar Cayley graphs: results and problems
Классические графы Кэли для групп давно и основательно зарекомендовали себя в решении прикладных задач, найдя применение в различных научных сферах, от криптографии до кампанологии. В последнее время всё большее внимание привлекает изучение прикладных аспектов графов Кэли полугрупп. В настоящей работе дан обзор результатов, полученных при исследованиях полугрупп с планарными графами Кэли, и результатов по изучению ранга планарности многообразий полугрупп. Сформулирован ряд нерешённых проблем, решение которых найдёт применение в комбинаторной теории полугрупп. В заключении даётся понятие спектра рангов планарности многообразий полугрупп, с помощью которого появляется возможность хеширования полугрупповых многообразий
Multicoloured Random Graphs: Constructions and Symmetry
This is a research monograph on constructions of and group actions on
countable homogeneous graphs, concentrating particularly on the simple random
graph and its edge-coloured variants. We study various aspects of the graphs,
but the emphasis is on understanding those groups that are supported by these
graphs together with links with other structures such as lattices, topologies
and filters, rings and algebras, metric spaces, sets and models, Moufang loops
and monoids. The large amount of background material included serves as an
introduction to the theories that are used to produce the new results. The
large number of references should help in making this a resource for anyone
interested in beginning research in this or allied fields.Comment: Index added in v2. This is the first of 3 documents; the other 2 will
appear in physic
Algebraic and geometric aspects of two-dimensional Artin groups
In this thesis we study the algebra and the geometry of two-dimensional Artin groups under various aspects. First, we solve the problem of acylindrical hyperbolicity, by proving that all the two-dimensional Artin groups that are not trivially non-acylindrically-hyperbolic are acylindrically hyperbolic. In particular, we prove that every non-spherical Artin group of dimension 2 has trivial centre. Then, we study the structure of parabolic subgroups of large-type Artin groups, and prove various results about their combinatorial structure. We notably show that any intersection of parabolic subgroups is again a parabolic subgroup. Finally, we study the isomorphisms between Artin groups of large-type, and we prove that the family of large-type free-of-infnity Artin groups is rigid. We also fully describe the automorphism groups of these Artin groups
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science