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  • 1 Università di Pisa, Largo Bruno Pontecorvo, 5, 56127 PISA, Italy
  • | 2 Università di Bologna, Piazza di Porta San Donato, 5, 40126 BOLOGNA, Italy
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Abstract

To a branched cover f between orientable surfaces one can associate a certain branch datumD(f), that encodes the combinatorics of the cover. This D(f) satisfies a compatibility condition called the Riemann-Hurwitz relation. The old but still partly unsolved Hurwitz problem asks whether for a given abstract compatible branch datum D there exists a branched cover f such that D(f)=D. One can actually refine this problem and ask how many these f's exist, but one must of course decide what restrictions one puts on such f’s, and choose an equivalence relation up to which one regards them. As it turns out, quite a few natural choices for this relation are possible. In this short note we carefully analyze all these choices and show that the number of actually distinct ones is only three. To see that these three choices are indeed different from each other we employ Grothendieck's dessins d'enfant.

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Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

Managing Editor

Gábor SÁGI (Rényi Institute of Mathematics)

Editorial Board

  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
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2020  
Total Cites 536
WoS
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Impact Factor  
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without
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5 Year 1,703
Impact Factor
Journal  0,68
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Rank by Journal  Mathematics 230/470 (Q2)
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Citable 32
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Total 0
Reviews
Scimago 24
H-index
Scimago 0,307
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Scimago Mathematics (miscellaneous) Q3
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Scopus 139/130=1,1
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Scopus General Mathematics 204/378 (Q3)
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Scopus 1,069
SNIP  
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to acceptance  
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acceptance  
to publication  
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2019  
Total Cites
WoS
463
Impact Factor 0,468
Impact Factor
without
Journal Self Cites
0,468
5 Year
Impact Factor
0,413
Immediacy
Index
0,135
Citable
Items
37
Total
Articles
37
Total
Reviews
0
Cited
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Citing
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15,5
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0,196
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in
Citable Items
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Normalized
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Average
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23
Scimago
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0,234
Scopus
Scite Score
76/104=0,7
Scopus
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General Mathematics 247/368 (Q3)
Scopus
SNIP
0,671
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14%

 

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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation
1966
Publication
Programme
2021 Volume 58
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per Year
1
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Founder Magyar Tudományos Akadémia  
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ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)