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Infinite Log-Concavity and r-Factor |
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PP: 109-115 |
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Author(s) |
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Zahid Raza,
Anjum Ali,
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Abstract |
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| Uminsky and Yeats [D. Uminsky, and K. Yeats, electronic Journal of Combinatorics 14, 1-13 (2007)], studied the properties
of the log-operator L on the subset of the finite symmetric sequences and prove the existence of an infinite region R, bounded
by parametrically defined hypersurfaces such that any sequence corresponding a point of R is infinitely log-concave. We study the
properties of a new operator Lr and redefine the hypersurfaces which generalizes the one defined by Uminsky and Yeats.We show that
any sequence corresponding a point of the region Rr, bounded by the new generalized parametrically defined r-factor hypersurfaces, is
Generalized r-factor infinitely log concave. We also give an improved value of r◦ found by McNamara and Sagan [P. R.W. McNamara
and B. E. Sagan, Adv. App. Math., 44, 1-15 (2010)], as the log-concavity criterion using the new log-operator. |
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