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DTSTAMP:20260614T134951
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SUMMARY:Graduate Student Colloquium: Melissa Beerbower
DESCRIPTION:On the Lucky Sets of Fubini Rankings\nMelissa Beerbower\nLoyola University Chicago \nRecall that Fubini rankings of length n are rankings of n competitors allowing for ties. We can say that the number of rankings\, k\, with k less than or equal to n\, is equal to the number of lucky competitors. A lucky competitor is the first to attain its rank. We enumerate Fubini rankings recursively through fixed sets of lucky competitors. Also recall that unit Fubini rankings are Fubini rankings with at most two competitors for each rank. We enumerate unit Fubini rankings through fixed lucky sets. Our enumerations explain twin coefficients for minimum powers in the lucky polynomial of ell-interval Fubini rankings.
URL:https://uwm.edu/math/event/graduate-student-colloquium-melissa-beerbower/
LOCATION:EMS Building\, Room E495\, E495; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States
CATEGORIES:Graduate Student Colloquia
ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu
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SUMMARY:Colloquium: Dr. Rafael S. González D'León
DESCRIPTION:On Whitney numbers of the first and second kind\, or is it the other way around?\nDr. Rafael S. González D’León\nAssistant Professor \nLoyola University Chicago \nAlgebraic combinatorics is centered on the idea that a variety of algebraic objects can be understood using the tools from combinatorics. In this talk\, I will illustrate this idea using a modern example of how combinatorial theories can give us a better understanding on a subject. The story I will tell involves the Whitney numbers of the first and second kind\, which are a pair of invariants of partially ordered sets (posets) that are relevant in several areas of mathematics. One of their most interesting appearances is as the coefficients of a polynomial enumerating proper colorings of a graph (think of colorings of a map where neighboring countries must be distinguishable from each other). They also appear counting regions in the complement of a real hyperplane arrangement. \nI will introduce and give insight into the algebraic and combinatorial objects in this story and share a very curious phenomenon: sometimes the Whitney numbers of the first and second kind of a poset are also the Whitney numbers of the second and first kind\, but of a different poset. Some recent results about this phenomenon could shed light on longstanding questions in the subject.
URL:https://uwm.edu/math/event/colloquium-dr-rafael-s-gonzalez-dleon/
LOCATION:EMS Building\, E495\, 3200 N Cramer St\, Milwaukee\, WI\, United States
CATEGORIES:Colloquia
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