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SUMMARY:Helena Bergold (Freie Universität Berlin)
DTSTART:20240419T130000Z
DTEND:20240419T140000Z
DTSTAMP:20260423T004550Z
UID:ACPMS/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ACPMS/39/">A
 n Extension Theorem for Signotopes</a>\nby Helena Bergold (Freie Universit
 ät Berlin) as part of Algebraic and Combinatorial Perspectives in the Mat
 hematical Sciences\n\n\nAbstract\nIn 1926\, Levi showed that\, for every p
 seudoline arrangement $A$ and two\npoints in the plane\, $A$ can be extend
 ed by a pseudoline which contains\nthe two prescribed points. Later extend
 ability was studied for\narrangements of pseudohyperplanes in higher dimen
 sions. While the\nextendability of an arrangement of proper hyperplanes in
  R^d with a\nhyperplane containing $d$ prescribed points is trivial\, Rich
 ter-Gebert\nfound an arrangement of pseudoplanes in R^3 which cannot be ex
 tended\nwith a pseudoplane containing two particular prescribed points.\nI
 n this talk\, we investigate the extendability of signotopes\, which are\n
 a combinatorial structure encoding a rich subclass of pseudohyperplane\nar
 rangements. We show that signotopes of odd rank are extendable in the\nsen
 se that for two prescribed crossing points we can add an element\ncontaini
 ng them.\n
LOCATION:https://researchseminars.org/talk/ACPMS/39/
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