Log-concavity and lc-positivity
WitrynaWe also introduce the concept of q-log-convexity and establish the link with linear transformations preserving the log-convexity. MSC: 05A20; 11B73; 11B83; 11B37 ... Log-concavity and LC-positivity by Yi Wang, Yeong-nan Yeh - … WitrynaExamples of double LC-positive triangles include the constant triangle and the Pascal triangle. We also give a generalization of a result of Liggett that is used to prove a conjecture of Pemantle on characteristics of negative dependence.
Log-concavity and lc-positivity
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Witryna8 kwi 2005 · Abstract: A triangle $\{a(n,k)\}_{0\le k\le n}$ of nonnegative numbers is LC-positive if for each $r$, the sequence of polynomials $\sum_{k=r}^n a(n,k)q^k$ is $q$ … WitrynaLog-concavity and LC-positivity. Article. Feb 2007; Wang Yi; Yeong-nan Yeh; A triangle {a(n,k)}0⩽k⩽n of nonnegative numbers is LC-positive if for each r, the sequence of polynomials is q-log ...
Witryna8 kwi 2005 · Title: Log-concavity and LC-positivity. Authors: Yi Wang, Yeong-Nan Yeh. Download PDF Abstract: ... WitrynaA triangle {a(n,k)}0≤k≤n of nonnegative numbers is LC-positive if for each r, the sequence of polynomials ∑nk=ra(n,k)qk is q-log-concave. It is double LC-positive if both triangles {a(n,k)} and {a(n,n−k)} are LC-positive. We show that if {a(n,k)} is LC-positive then the log-concavity of the sequence {xk} implies that of the sequence {zn} defined by …
Witryna1 lis 2013 · We show that if {a(n,k)} is LC-positive then the log-concavity of the sequence {xk} implies that of the sequence {zn} defined by , and if {a(n,k)} is double … WitrynaA triangle {a(n,k)}0≤k≤n of nonnegative numbersis LC-positive if for each r, the sequence of polynomials Pn k=r a(n,k)q k is q-log-concave. It is double LC-positive if both …
WitrynaAbstract. A triangle {a(n, k)}0≤k≤n of nonnegative numbers is LC-positive if for each r, the sequence of polynomials ∑ n k=r a(n, k)qk is q-log-concave. It is double LC-positive if …
Witryna11 maj 2024 · In this paper, we propose the generalized triangles called s-triangles for s given positive integer, as a bi-indexed sequence of nonnegative numbers {a s (n, k)} … download image of carWitryna5 mar 2024 · It is a good way to obtain the log-concavity or log-convexity by some operators. For instance, Davenport and Pólya ... Log-concavity and LC-positivity. J. Comb. Theory A 114, 195–210 (2007) MathSciNet MATH Google Scholar Wang, Y., Yeh, Y.-N.: Polynomials with real zeros and P ólya frequency sequences. J. Comb. Theory … class 6 chapter 6 civics pdfWitryna1 lut 2007 · Since the array a (k, j) is LC-positive for q ≥ 1, in order to establish the log-concavity of the sequence b k , it is enough to show that the sequence c j = (−1) j (m … class 6 cbse math worksheetWitryna8 kwi 2005 · Examples of double LC-positive triangles include the constant triangle and the Pascal triangle. We also give a generalization of a result of Liggett that is used to prove a conjecture of Pemantle on characteristics of negative dependence. download imagens svgWitryna1 paź 2007 · This paper is devoted to the study of the log-convexity of combinatorial sequences. We show that the log-convexity is preserved under componentwise sum, under binomial convolution, and by the linear transformations given by the matrices of binomial coefficients and Stirling numbers of two kinds. class 6 ch 6 maths notesWitryna30 sty 2010 · In addition, we prove the strong q-log-concavity of the q-Narayana numbers. The q-log-concavity of the q-Narayana numbers N q (n,k) for fixed k is a special case of a conjecture of McNamara and Sagan on the infinite q-log-concavity of the Gaussian coefficients. ... Log-concavity and LC-positivity. J. Comb. Theory Ser. … class 6 ch 6 geographyWitryna8 kwi 2005 · A triangle of nonnegative numbers is LC-positive if for each , the sequence of polynomials is -log-concave. It is double LC-positive if both triangles and are LC-positive. We show that if is LC-positive then the log-concavity of the sequence … download image of computer