Totally positive matrices, Polya frequency sequences, and Schur polynomials

Abstract: I will discuss totally positive/non-negative matrices and kernels, including Polya frequency (PF) functions and sequences. This includes examples, history, and basic results on total positivity, variation diminution, sign non-reversal, and generating functions of PF sequences (with some proofs). I will end with applications of total positivity to old and new phenomena involving Schur polynomials.

classical analysis and ODEscombinatoricsnumber theory

Audience: researchers in the topic

Special Functions and Number Theory seminar

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