18 citations · 28 across the 12 of their papers we have counts for
10 papers · 1 filter
Lascoux series, parking functions and noncrossing partitions
Alice L. L. Gao, Xin-Bei Liu, Arthur L. B. Yang +1
In the study of the generating series of Demazure characters, Lascoux used isobaric divided differences to define a family of polynomials indexed by permutations…
A simple proof of higher order Turán inequalities for Boros-Moll sequences
James Jing Yu Zhao
Recently, the higher order Turán inequalities for the Boros-Moll sequences were obtained by Guo. In this paper, we show a different approach to this resu…
On the positive zeros of generalized Narayana polynomials related to the Boros-Moll polynomials
James J. Y. Zhao
The generalized Narayana polynomials arose from the study of infinite log-concavity of the Boros-Moll polynomials. The real-rootedness of had been proved…
Perron-Frobenius Theorem for Rectangular Tensors and Directed Hypergraphs
Linyuan Lu, Arthur L. B. Yang, James J. Y. Zhao
For any positive integers , , , , an -order -dimensional rectangular tensor ${\cal A}=(a_{i_1\cdots i_r}^{j_1\cdots j_s}) \in ({\mathbb R}^n)^r\times ({\m…
Log-behavior of two sequences related to the elliptic integrals
Brian Y. Sun, James J. Y. Zhao
Two interesting sequences arose in the study of the series expansions of the complete elliptic integrals, which are called the Catalan-Larcombe-French sequence …
Sun's log-concavity conjecture on the Catalan-Larcombe-French sequence
James J. Y. Zhao
Let 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…
Log-concavity of the Fennessey-Larcombe-French Sequence
Arthur L. B. Yang, James J. Y. Zhao
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…
A determinant representation for generalized ballot and Fuss-Catalan numbers
James J. Y. Zhao
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, wh…
Koroljuk's formula for counting lattice paths revisited
James J. Y. Zhao
Koroljuk gave a summation formula for counting the number of lattice paths from to with -steps in the plane that stay strictly above the line $y=k(x-d…
A combinatorial proof of the Alladi-Gordon key identity for Schur's partition theorem
James J. Y. Zhao
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 o…