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SUMMARY:Halil İbrahim Karakaş (Başkent)
DTSTART:20251107T124000Z
DTEND:20251107T134000Z
DTSTAMP:20260423T021259Z
UID:OBAGS/72
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OBAGS/72/">O
 n the enumeration of Arf numerical semigroups with given multiplicity and 
 conductor</a>\nby Halil İbrahim Karakaş (Başkent) as part of ODTU-Bilke
 nt Algebraic Geometry Seminars\n\n\nAbstract\nThe number of numerical semi
 groups with given Frobenious number (or conductor\, or genus) is one of th
 e topics that is studied by many researchers. In our previous works\, we h
 ave given parametrizations of Arf numerical semigroups of small multiplici
 ty and obtained formulas for the number of Arf numerical semigroups with m
 ultiplicity less than 14 and arbitrary conductor. I presented part of thes
 e results in ODTÜ-Bikent AG seminars 6 years ago. We noticed that the num
 ber of Arf numerical semigroups with multiplicity $m$  and conductor $c$  
 is (eventually) constant for some $m$ (especially for prime $m$) when rest
 ricted to some congruence classes of $c$ modulo $m$. In a recent work with
  N. Tutaş\, we have characterized those multiplicities $m$ and congruence
  classes of $c$ modulo $m$ for which the above property holds. This talk w
 ill be based on [Karakaş H İ and Tutaş N\, (2025)\, On the enumeration 
 of Arf numerical semigroups with given multiplicity and conductor\, Semigr
 oup Forum 110\, 308-316.] where the above characterization is given.\n
LOCATION:https://researchseminars.org/talk/OBAGS/72/
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