BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Criel Merino (Instituto de Matematicas UNAM) DTSTART:20221013T190000Z DTEND:20221013T200000Z DTSTAMP:20260423T035813Z UID:Matroids/4 DESCRIPTION:Title: The h-vector of a matroid complex\, paving matroids and the chip firing g ame.\nby Criel Merino (Instituto de Matematicas UNAM) as part of Matro ids - Combinatorics\, Algebra and Geometry Seminar\n\nLecture held in Room 210 The Fields Institute.\n\nAbstract\nA non-empty set of monomials $\\Si gma$ is a multicomplex if for any monomial $z$ in $\\Sigma$ and a monomial $z'$ such that $z'|z$\, we have that $z'$ also belongs to $\\Sigma$. A mu lticomplex $\\Sigma$ is called pure if all its maximal elements have the s ame degree. This notion is a generalization of the simplicial complex\, an d several invariants extend directly\, as the $f$-vector of a multicomplex \, which is the vector that lists the monomials grouped by degrees. A non- empty set of monomials $\\Sigma$ is a multicomplex if for any monomial $z$ in $\\Sigma$ and a monomial $z'$ such that $z'|z$\, we have that $z'$ als o belongs to $\\Sigma$. A multicomplex $\\Sigma$ is called pure if all its maximal elements have the same degree. This notion is a generalization of the simplicial complex\, and several invariants extend directly\, as the $f$-vector of a multicomplex\, which is the vector that lists the monomial s grouped by degrees. The relevance of multicomplexes in matroid theory is partly due to a 1977 Richard Stanley conjecture that says that the $h$-ve ctor of a matroid complex is the $f$-vector of a pure multicomplex. This h as been proved for several families of matroids. In this talk\, we review some results of Stanley’s conjecture\, mainly for paving and cographic m atroids. A paving matroid is one in which all its circuits have a size of at least the rank of the matroid. While\, the chip firing game is a solita ire game played on a connected graph $G$ that surprisingly is related to t he $h$-vector of the bond matroid of $G$.\n LOCATION:https://researchseminars.org/talk/Matroids/4/ END:VEVENT END:VCALENDAR