Kvazikrovi in delovanje končnih grup na grafih, II / Quasi-coverings and Finite Group Actions on Graphs, II
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Naziv Tittle |
Kvazikrovi in delovanje končnih grup na grafih, II / Quasi-coverings and Finite Group Actions on Graphs, II |
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Akronim Acronim |
BI-RU/16-18-015 |
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Opis Description |
(SI) Poiskati želimo formulo za strukturo Jacobijeve grupe za Cayleyeve grafe cikličnih in diedrskih grip.Pričakujemo, da bomo dobili rezultate, ki se izražajo s polinomi Čebyševa v odvisnosti od kompleksne spremenljivke. Obravnavali bomo lastnosti grupe avtomorfizmov grafov in matroidov s coljem dobiti nekaj verzij Riemann-Hurwitzovih formul za oceno reda grup avtomorfizmov. Poiskali bomo diskretno analogijo klasičnih izrekov za Riemannove ploskve, ki so jih dokazali R. Accola, W. Harvey in C. Maclachlan. Izračunali bomo število cikličnih krovov z razvejitvami in predpisanim tipom razvejitev danega grafa. Z uporabo simetrijskih lastnosti grafov iz njihovo prestavitvijo v obliki policirkulantov ali drugih krovnih grafov (npr. kot Haarove grafe) bomo shranjevali njihove kvociente grafe in tako prihranili prostor različnih cenzusov. (EN) Find an explicit formula for the structure of the Jacobian group for the Caley graphs of cyclic and dihedral groups. We suppose to give the results in terms of Chebishev polymonial, in general depending on complex variable. The aim is obtain a few version of the Riemann-Hurwitz formulas and find Hurwitz tipe estimates for the size of automorphism group. We are going to calculate the number of cyclic branched covering of graphs with prescribed ramification type. This a discrete version of the Hurwitz enumeration problem for Riemann surfaces. We are going to exploit symmetry properties of graphs to represent them as polycirculants or other coverings of graphs (e.g. Haar graphs) and store quotient graphs in order to save space in various graph censuses. |
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Trajanje Duration |
01/10/2016 - 30/09/2018 |
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Vodja projekta Project Leader |
Tomaž Pisanski |
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Sodelujoče organizacije Participating organizations |
Sobolev Institute of Mathematics, Novosibirsk, Russia |
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Oddelek Department |
Oddelek za matematiko IAM |