Akcijski grafi in tehnike krovnih grafov / Action graphs and covering graph techniques
|
Naziv Tittle |
Akcijski grafi in tehnike krovnih grafov / Action graphs and covering graph techniques |
|
Akronim Acronim |
J1-9187 |
|
Opis Description |
(SI) Projekt bo razvil in uporabljal nabor močnih, novih metod diskretne matematike in teoretičnega računalništva v povezavi s teorijo grup, diskretno geometrijo in algebraično topologijo v naskoku na številne pomembne odprte probleme. Med pomembnejšimi problemi sta razvoj teorije grafov delovanj in nadaljnji napredki pri tehnikah krovnih grafov. Posplošeni grafi delovanj, kot jih definiramo, posplošujejo številne pomembne matematične koncepte, kot so Cayleyjevi barvni grafi grup, monodromne grupe zemljevidov in hiperzemljevidov na ploskvah, permutacijsko-involucijski opis orientabilnih zemljevidov na ploskvah, abstraktni politopi in manipleksi. Za nas je graf delovanja končna množica praporov, opremljenih z zbirko permutacij in zbirko involucij. Z uporabo regularnih krovnih projekcij dobimo tako imenovane simetrijske tipe grafov, ki zaobjamejo bistvo simetrij v prvotnih grafih delovanj. Z uporabo tega pojma in naše nedavne teorije reprezentacij grafov dobimo močno orodje za proučevanje vprašanja geometrične in topološke realizacije določenih kombinatoričnih objektov. (EN) The project will develop and employ a toolbox of powerful new methods in discrete mathematics in connection with group theory, discrete geometry, algebraic topology, which will be used for attacking several outstanding open problems. In particular a theory of action graphs and further advance of the covering graph techniques will be developed. Generalized action graphs, as we define them, generalize a number of important mathematical concepts such as Cayley color graphs of groups, monodromy groups of maps and hyper-maps on surfaces, permutation-involution description of oriented maps on surfaces, abstract polytopes and maniplexes. For us, an action graph is a finite set of flags, endowed with a collection of permutations and another collection of involutions. By using regular covering projections we obtain the so-called symmetry type graphs that capture the essence of symmetries of the original action graphs. This, combined with our recent theory of representation of graphs, will be a powerful tool for studying geometric and topological realizability questions of certain combinatorial objects. Also, we started a theory of arc types for vertex-transitive graphs, which we intend to apply towards the solution of the poly-circulant conjecture. |
|
Vrsta projekta Project Type |
Temeljni projekt |
|
Trajanje Duration |
01/07/2018 - 30/06/2021 |
|
URL URL |
https://www.sicris.si/public/jqm/search_basic.aspx?lang=slv&opdescr=search&opt=2&subopt=1&code1=cmn&code2=auto&search_term=J1-9187 |
|
Vodja projekta Project Leader |
Tomaž Pisanski |
|
Sodelujoče organizacije Participating organizations |
Inštitut za matematiko, fiziko in mehaniko; UL Fakulteta za matematiko in fiziko |
|
Oddelek Department |
Oddelek za Informacijske Znanosti in Tehnologije IAM |