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SUMMARY:Gunnar Fløystad (University of Bergen)
DTSTART:20250214T140000Z
DTEND:20250214T150000Z
DTSTAMP:20260423T004546Z
UID:ACPMS/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ACPMS/48/">S
 ubmodular functions\, generalized permutahedra\, conforming preorders\, an
 d cointeracting bialgebras</a>\nby Gunnar Fløystad (University of Bergen)
  as part of Algebraic and Combinatorial Perspectives in the Mathematical S
 ciences\n\n\nAbstract\nGeneralized permutahedra (GP) is a central class of
  polyhedra with surprisingly many connections to various areas. Examples a
 re matroid polytopes and and \npolymatroids. GP are also equivalent to sub
 modular functions\, an\nimportant class in optimization and economics.\n\n
 To a submodular function we:\nDefine a class of preorders\, conforming pre
 orders\nWe show the faces of a GP are in bijection with the conforming pre
 orders.\nThe face poset structure of the GP induces two order relations on
  conforming preorders\, subdivision and contraction\, and we investigate t
 heir properties.\nThere is Hopf monoid of submodular functions. We show it
  has a bimonoid of modular functions cointeracting in a non-standard way. 
 By recent theory of L.Foissy this associates a canonical polynomial to any
  submodular function.\n
LOCATION:https://researchseminars.org/talk/ACPMS/48/
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