Log-concavity and strong q-log-convexity for Riordan arrays and recursive matrices

Let [An,k ] n,k [egs]0 be an infinite lower triangular array satisfying the recurrencefor n [egs] 1 and k [egs] 0, where A 0,0 = 1, A 0,k = A k,-1 = 0 for k > 0. We present some criteria for the log-concavity of rows and strong q-log-convexity of generating functions of rows. Our results can be a...
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Gespeichert in:

Autor*in:	Bao-Xuan Zhu [verfasserIn]

Format:	Artikel
Sprache:	Englisch

Erschienen:	2017

Schlagwörter:	Concavity Convexity Pascal (programming language) Triangles Transformations

Übergeordnetes Werk:	Enthalten in: Proceedings / A - Edinburgh : Soc., 1943, 147(2017), 6, Seite 1297
Übergeordnetes Werk:	volume:147 ; year:2017 ; number:6 ; pages:1297

Links:	Volltext Link aufrufen

DOI / URN:	10.1017/S0308210516000500

Katalog-ID:	OLC1998687163

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title	Log-concavity and strong q-log-convexity for Riordan arrays and recursive matrices
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title_full	Log-concavity and strong q-log-convexity for Riordan arrays and recursive matrices
author_sort	Bao-Xuan Zhu
journal	Proceedings / A
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lang_code	eng
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container_start_page	1297
author_browse	Bao-Xuan Zhu
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class	510 DNB
format_se	Aufsätze
author-letter	Bao-Xuan Zhu
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title_sort	log-concavity and strong q-log-convexity for riordan arrays and recursive matrices
title_auth	Log-concavity and strong q-log-convexity for Riordan arrays and recursive matrices
abstract	Let [An,k ] n,k [egs]0 be an infinite lower triangular array satisfying the recurrencefor n [egs] 1 and k [egs] 0, where A 0,0 = 1, A 0,k = A k,-1 = 0 for k > 0. We present some criteria for the log-concavity of rows and strong q-log-convexity of generating functions of rows. Our results can be applied to many well-known triangular arrays, such as the Pascal triangle, the Stirling triangle of the second kind, the Bell triangle, the large Schröder triangle, the Motzkin triangle, and the Catalan triangles of Aigner and Shapiro, in a unified approach. In addition, we prove that the binomial transformation not only preserves the strong q-log-convexity property, but also preserves the strong q-log-concavity property. Finally, we demonstrate that the strong q-log-convexity property is preserved by the Stirling transformation and Whitney transformation of the second kind, which extends some known results for the strong q-log-convexity property.
abstractGer	Let [An,k ] n,k [egs]0 be an infinite lower triangular array satisfying the recurrencefor n [egs] 1 and k [egs] 0, where A 0,0 = 1, A 0,k = A k,-1 = 0 for k > 0. We present some criteria for the log-concavity of rows and strong q-log-convexity of generating functions of rows. Our results can be applied to many well-known triangular arrays, such as the Pascal triangle, the Stirling triangle of the second kind, the Bell triangle, the large Schröder triangle, the Motzkin triangle, and the Catalan triangles of Aigner and Shapiro, in a unified approach. In addition, we prove that the binomial transformation not only preserves the strong q-log-convexity property, but also preserves the strong q-log-concavity property. Finally, we demonstrate that the strong q-log-convexity property is preserved by the Stirling transformation and Whitney transformation of the second kind, which extends some known results for the strong q-log-convexity property.
abstract_unstemmed	Let [An,k ] n,k [egs]0 be an infinite lower triangular array satisfying the recurrencefor n [egs] 1 and k [egs] 0, where A 0,0 = 1, A 0,k = A k,-1 = 0 for k > 0. We present some criteria for the log-concavity of rows and strong q-log-convexity of generating functions of rows. Our results can be applied to many well-known triangular arrays, such as the Pascal triangle, the Stirling triangle of the second kind, the Bell triangle, the large Schröder triangle, the Motzkin triangle, and the Catalan triangles of Aigner and Shapiro, in a unified approach. In addition, we prove that the binomial transformation not only preserves the strong q-log-convexity property, but also preserves the strong q-log-concavity property. Finally, we demonstrate that the strong q-log-convexity property is preserved by the Stirling transformation and Whitney transformation of the second kind, which extends some known results for the strong q-log-convexity property.
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container_issue	6
title_short	Log-concavity and strong q-log-convexity for Riordan arrays and recursive matrices
url	http://dx.doi.org/10.1017/S0308210516000500 https://search.proquest.com/docview/1966053663
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up_date	2024-07-04T05:29:57.121Z
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