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pro vyhledávání: '"Zhao, James J. Y."'
Autor:
Zhao, James J. Y.
Let $U_{n,d}$ be the uniform matroid of rank $d$ on $n$ elements. Denote by $g_{U_{n,d}}(t)$ the Speyer's $g$-polynomial of $U_{n,d}$. The Tur\'{a}n inequality and higher order Tur\'{a}n inequality are related to the Laguerre-P\'{o}lya ($\mathcal{L}$
Externí odkaz:
http://arxiv.org/abs/2409.08085
Autor:
Zhao, James J. Y.
The Boros-Moll sequences $\{d_\ell(m)\}_{\ell=0}^m$ arise in the study of evaluation of a quartic integral. After the infinite log-concavity conjecture of the sequence $\{d_\ell(m)\}_{\ell=0}^m$ was proposed by Boros and Moll, a lot of interesting in
Externí odkaz:
http://arxiv.org/abs/2406.13790
Autor:
Zhao, James J. Y.
The generalized Narayana polynomials $N_{n,m}(x)$ arose from the study of infinite log-concavity of the Boros-Moll polynomials. The real-rootedness of $N_{n,m}(x)$ had been proved by Chen, Yang and Zhang. They also showed that when $n\geq m+2$, each
Externí odkaz:
http://arxiv.org/abs/2108.03590
For any positive integers $r$, $s$, $m$, $n$, an $(r,s)$-order $(n,m)$-dimensional rectangular tensor ${\cal A}=(a_{i_1\cdots i_r}^{j_1\cdots j_s}) \in ({\mathbb R}^n)^r\times ({\mathbb R}^m)^s$ is called partially symmetric if it is invariant under
Externí odkaz:
http://arxiv.org/abs/1804.08582
Autor:
Sun, Brian Y., Zhao, James J. Y.
Two interesting sequences arose in the study of the series expansions of the complete elliptic integrals, which are called the Catalan-Larcombe-French sequence $\{P_n\}_{n\geq 0}$ and the Fennessey-Larcombe-French sequence $\{V_n\}_{n\geq 0}$ respect
Externí odkaz:
http://arxiv.org/abs/1602.04359
Autor:
Zhao, James J. Y.
Let $\{P_n\}_{n\geq 0}$ denote the Catalan-Larcombe-French sequence, which naturally came up from the series expansion of the complete elliptic integral of the first kind. In this paper, we prove the strict log-concavity of the sequence $\{\sqrt[n]{P
Externí odkaz:
http://arxiv.org/abs/1505.06650
Autor:
Yang, Arthur L. B., Zhao, James J. Y.
We prove the log-concavity of the Fennessey-Larcombe-French sequence based on its three-term recurrence relation, which was recently conjectured by Zhao. The key ingredient of our approach is a sufficient condition for log-concavity of a sequence sub
Externí odkaz:
http://arxiv.org/abs/1503.02151
Autor:
Zhao, James J. Y.
In this note we introduce a determinant and then give its evaluating formula. The determinant turns out to be a generalization of the well-known ballot and Fuss-Catalan numbers, which is believed to be new. The evaluating formula is proved by showing
Externí odkaz:
http://arxiv.org/abs/1312.3164
Autor:
Zhao, James J. Y.
Koroljuk gave a summation formula for counting the number of lattice paths from $(0,0)$ to $(m,n)$ with $(1,0), (0,1)$-steps in the plane that stay strictly above the line $y=k(x-d)$, where $k$ and $d$ are positive integers. In this paper we obtain a
Externí odkaz:
http://arxiv.org/abs/1306.6015
Autor:
Zhao, James J. Y.
The Alladi-Gordon identity plays an important role for the Alladi-Gordon generalization of Schur's partition theorem. By using Joichi-Stanton's insertion algorithm, we present an overpartition interpretation for the Alladi-Gordon key identity. Based
Externí odkaz:
http://arxiv.org/abs/1202.1219