Infinite log-concavity for polynomial pólya frequency sequences
2015 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 143, no 12, 5147-5158 p.Article in journal (Refereed) PublishedText
McNamara and Sagan conjectured that if a0, a1, a2, . . . is a Pólya frequency (PF) sequence, then so is (formula presented), . . .. We prove this conjecture for a natural class of PF-sequences which are interpolated by polynomials. In particular, this proves that the columns of Pascal’s triangle are infinitely log-concave, as conjectured by McNamara and Sagan. We also give counterexamples to the first mentioned conjecture. Our methods provide families of nonlinear operators that preserve the property of having only real and nonpositive zeros.
Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2015. Vol. 143, no 12, 5147-5158 p.
Infinite log-concavity, Log-concavity, Pólya frequency sequence, Real zeros
IdentifiersURN: urn:nbn:se:kth:diva-181260DOI: 10.1090/proc/12654ISI: 000364413200011ScopusID: 2-s2.0-84944198620OAI: oai:DiVA.org:kth-181260DiVA: diva2:900895
QC 201602052016-02-052016-01-292016-02-05Bibliographically approved