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Correction to a Theorem on Total Positivity

Published online by Cambridge University Press:  20 November 2018

Carl Johan Ragnarsson ,
Wesley Wai Suen  and
David G. Wagner
Carl Johan Ragnarsson
Affiliation:
Pålsjövägen 16, SE-22363 Lund, Sweden e-mail: cjr@gongames.com
Wesley Wai Suen
Affiliation:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, N2L 3G1 e-mail: wwsuen@math.uwaterloo.cadgwagner@math.uwaterloo.ca
David G. Wagner
Affiliation:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, N2L 3G1 e-mail: wwsuen@math.uwaterloo.cadgwagner@math.uwaterloo.ca
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Abstract

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A well-known theorem states that if $f\left( z \right)$ generates a $\text{P}{{\text{F}}_{r}}$ sequence then $1/f\left( -z \right)$ generates a $\text{P}{{\text{F}}_{r}}$ sequence. We give two counterexamples which show that this is not true, and give a correct version of the theorem. In the infinite limit the result is sound: if $f\left( z \right)$ generates a $\text{PF}$ sequence then $1/f\left( -z \right)$ generates a $\text{PF}$ sequence.

Keywords

15A4815A4515A5705E05Total positivityToeplitz matrixPólya frequency sequenceskew Schur function
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 2 , 01 June 2006 , pp. 281 - 284
Copyright
Copyright © Canadian Mathematical Society 2006

References

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