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Experimental Mathematics Seminar

From Stern's triangle to upper homogeneous posets

Richard Stanley, MIT and the University of Miami

Location:  via Zoom: link [password: 6564120420 ]
Date & time: Thursday, 19 November 2020 at 5:00PM - 6:00PM

Abstract: Stern's triangle S is an array of numbers similar to Pascal's triangle, except that in addition to adding two adjacent numbers we also copy each number down to the next row. We discuss some arithmetic properties of S that can be greatly generalized. There is also a natural poset P associated to S. This poset is upper homogeneous, i.e., for every t in P, the subposet {s: s ? t} is isomorphic to P. As a consequence, the Ehrenborg quasisymmetric function of P, which is a kind of generating function for counting certain chains in P, is a symmetric function. This motivates the question of which symmetric functions can be Ehrenborg quasisymmetric functions of upper homogeneous posets.

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