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SUMMARY:Olivier Bernardi (Brandeis University)
DTSTART:20221018T190000Z
DTEND:20221018T200000Z
DTSTAMP:20260423T040106Z
UID:Matroids/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Matroids/5/"
 >Universal Tutte polynomial</a>\nby Olivier Bernardi (Brandeis University)
  as part of Matroids - Combinatorics\, Algebra and Geometry Seminar\n\nLec
 ture held in Room 210 The Fields Institute.\n\nAbstract\nThe Tutte polynom
 ial is an important matroid invariant.  We will explain a natural way to e
 xtend the Tutte polynomial from matroids to polymatroids. The Tutte polyno
 mial can then be expressed as a sum over the points of the polymatroid (th
 is is an extension of the basis extension of the classical definition of  
 the Tutte polynomial in terms of activities). Our definition is related to
  previous works of Cameron and Fink and of Kálmán and Postnikov. \n\nOne
  of the great properties of our Tutte polynomial is that it is polynomial 
 in the values of the rank function of the polymatroid. In other words\, we
  can define a "universal Tutte polynomial" $T_n$ in $2+(2^n−1)$ variable
 s that specialize to the Tutte polynomials of all polymatroids on n elemen
 ts (the $2^n-1$ extra variables correspond to the non-trivial values of th
 e rank function). \n\nThis is joint work with Tamás Kálmán and Alex Pos
 tnikov.\n
LOCATION:https://researchseminars.org/talk/Matroids/5/
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