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Friday, April 05, 2019
12:00 PM - 1:00 PM
Linde Hall 255

Math Graduate Student Seminar

Path counting and rank gaps in differential posets
Praveen Venkataramana, Department of Mathematics, Caltech,

We study the gaps Δp_n between consecutive rank sizes in r-differential posets by introducing a projection operator whose matrix entries can be expressed in terms of the number of certain paths in the Hasse diagram. We strengthen Miller's result that Δp_n≥1, which resolved a longstanding conjecture of Stanley, by showing that Δp_n≥2r. We also obtain stronger bounds in the case that the poset has many substructures called threads. (joint work with Christian Gaetz)

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