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DTSTART:20260308T070000
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DTSTART:20261101T060000
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DTSTART;TZID=America/Toronto:20261105T143000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-seminar-sophie
SUMMARY:Algebraic and Enumerative Combinatorics Seminar | Sophie Rehberg\,\
 nChromatic word-quasisymmetric functions of matroids
CLASS:PUBLIC
DESCRIPTION:SPEAKER:\n Sophie Rehberg\n\nAFFILIATION:\n University of Water
 loo\n\nLOCATION:\n MC 5417\n\nABSTRACT: Billera\, Jia\, and Reiner (2009)
  introduced the\nquasisymmetric functions of matroids and showed that this
  defines a\nHopf algebra homomorphism which is a valuative invariant\, i.e
 .\,\nisomorphic matroids have the same quasisymmetric function and\npolyto
 pal decompositions of matroid base polytopes define relations\namong the c
 orresponding quasisymmetric functions. In this project we\nstudy an analog
 ue in non-commuting variables\, the word-quasisymmetric\nfunctions. To eve
 ry matroid M we associate a word-quasisymmetric\nfunction ψ(M) and call t
 his the chromatic word-quasisymmetric\nfunctions of a matroid. Matroids an
 d word-quasisymmetric functions\nform Hopf algebras\, and our map ψ betwe
 en them is a homomorphism. We\nwant to study the kernel\, equivalently the
  image\, of the map ψ from\nmatroids to word-quasisymmetric functions\, t
 hat is\, we would like to\nunderstand which matroids are indistinguishable
  by the chromatic\nword-quasisymmetric functions. The map ψ is not an inv
 ariant\, but we\ncan show that it is valuative. Using Schubert matroids an
 d nested\nmatroids\, special classes of matroids\, we prove a lower bound 
 of 2^d\n− d for the rank of the map ψ from matroids to the chromatic\nw
 ord-quasisymmetric functions in degree d and conjectured the upper\nbound 
 of d! is tight. Recent AI supported work shows that our\nconjecture is tru
 e.\n\nThis is joint work with Raul Penaguiao.\n\nThere will be a pre-semin
 ar presenting relevant background at\nbeginning graduate level starting at
  1:30pm in MC 5417.
DTSTAMP:20261102T154810Z
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