77 research outputs found
Dessins, their delta-matroids and partial duals
Given a map on a connected and closed orientable surface, the
delta-matroid of is a combinatorial object associated to which captures some topological information of the embedding. We explore how
delta-matroids associated to dessins d'enfants behave under the action of the
absolute Galois group. Twists of delta-matroids are considered as well; they
correspond to the recently introduced operation of partial duality of maps.
Furthermore, we prove that every map has a partial dual defined over its field
of moduli. A relationship between dessins, partial duals and tropical curves
arising from the cartography groups of dessins is observed as well.Comment: 34 pages, 20 figures. Accepted for publication in the SIGMAP14
Conference Proceeding
Catalog of dessins d'enfants with \le 4 edges
In this work all the dessins d'enfant with no more than 4 edges are listed
and their Belyi pairs are computed. In order to enumerate all dessins the
technique of matrix model computations was used. The total number of dessins is
134; among them 77 are spherical, 53 of genus 1 and 4 of genus 2. The orders of
automorphism groups of all the dessins are also found.
Dessins are listed by the number of edges. Dessins with the same number of
edges are ordered lexicographically by their lists of 0-valencies. The
corresponding matrix model for any list of 0-valencies is given and computed.
Complex matrix models for dessins with 1 -- 3 edges are used. For the dessins
with 4 edges we use Hermitian matrix model, correlators for which are computed
in [1].Comment: 64 pages, 134 figure
Notes for genera: basal clades of Fungi (including Aphelidiomycota, Basidiobolomycota, Blastocladiomycota, Calcarisporiellomycota, Caulochytriomycota, Chytridiomycota, Entomophthoromycota, Glomeromycota, Kickxellomycota, Monoblepharomycota, Mortierellomycota, Mucoromycota, Neocallimastigomycota, Olpidiomycota, Rozellomycota and Zoopagomycota)
Compared to the higher fungi (Dikarya), taxonomic and evolutionary studies on the basal clades of fungi are fewer in number. Thus, the generic boundaries and higher ranks in the basal clades of fungi are poorly known. Recent DNA based taxonomic studies have provided reliable and accurate information. It is therefore necessary to compile all available information since basal clades genera lack updated checklists or outlines. Recently, Tedersoo et al. (MycoKeys 13:1--20, 2016) accepted Aphelidiomycota and Rozellomycota in Fungal clade. Thus, we regard both these phyla as members in Kingdom Fungi. We accept 16 phyla in basal clades viz. Aphelidiomycota, Basidiobolomycota, Blastocladiomycota, Calcarisporiellomycota, Caulochytriomycota, Chytridiomycota, Entomophthoromycota, Glomeromycota, Kickxellomycota, Monoblepharomycota, Mortierellomycota, Mucoromycota, Neocallimastigomycota, Olpidiomycota, Rozellomycota and Zoopagomycota. Thus, 611 genera in 153 families, 43 orders and 18 classes are provided with details of classification, synonyms, life modes, distribution, recent literature and genomic data. Moreover, Catenariaceae Couch is proposed to be conserved, Cladochytriales Mozl.-Standr. is emended and the family Nephridiophagaceae is introduced
Methods of calculating radiative-conductive heat exchange in the components of electrovacuum instruments
- …