Results 1 to 10 of about 271 (37)

Refined ratio monotonicity of the coordinator polynomials of the root lattice of type Bn

Open Mathematics, 2023
Ratio monotonicity, a property stronger than both log-concavity and the spiral property, describes the behavior of the coefficients of many classical polynomials.
Su Xun-Tuan, Sun Fan-Bo
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A combinatorial proof of the Gaussian product inequality beyond the MTP2 case

Dependence Modeling, 2022
A combinatorial proof of the Gaussian product inequality (GPI) is given under the assumption that each component of a centered Gaussian random vector X=(X1,…,Xd){\boldsymbol{X}}=\left({X}_{1},\ldots ,{X}_{d}) of arbitrary length can be written as a ...
Genest Christian, Ouimet Frédéric
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The log-concavity of the q-derangement numbers of type B

Open Mathematics, 2018
Recently, Chen and Xia proved that for n ≥ 6, the q-derangement numbers Dn(q) are log-concave except for the last term when n is even. In this paper, employing a recurrence relation for DnB(q) $\begin{array}{} \displaystyle D^B_n(q) \end{array ...
Liu Eric H., Du Wenjing
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The hyperbolicity constant of infinite circulant graphs

Open Mathematics, 2017
If X is a geodesic metric space and x1, x2, x3 ∈ X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X.
Rodríguez José M., Sigarreta José M.
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Lorentzian polynomials on cones

Forum of Mathematics, Sigma
Inspired by the theory of hyperbolic polynomials and Hodge theory, we develop the theory of Lorentzian polynomials on cones. This notion captures the Hodge-Riemann relations of degree zero and one.
Petter Brändén, Jonathan Leake
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Zeros distribution and interlacing property for certain polynomial sequences

Open Mathematics
In this article, we first prove that the Hankel determinant of order three of the polynomial sequence {Pn(x)=∑k≥0P(n,k)xk}n≥0{\left\{{P}_{n}\left(x)={\sum }_{k\ge 0}P\left(n,k){x}^{k}\right\}}_{n\ge 0} is weakly (Hurwitz) stable, where P(n,k)P\left(n,k ...
Guo Wan-Ming
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Equality cases of the Alexandrov–Fenchel inequality are not in the polynomial hierarchy

Forum of Mathematics, Pi
Describing the equality conditions of the Alexandrov–Fenchel inequality [Ale37] has been a major open problem for decades. We prove that in the case of convex polytopes, this description is not in the polynomial hierarchy unless the polynomial hierarchy ...
Swee Hong Chan, Igor Pak
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Inequalities for higher order differences of the logarithm of the overpartition function and a problem of Wang-Xie-Zhang. [PDF]

Res Number Theory, 2023
Mukherjee G.
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Log-convexity and the overpartition function. [PDF]

Ramanujan J, 2023
Mukherjee G.
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New inequalities for p(n) and logp(n). [PDF]

Ramanujan J, 2023
Banerjee K, Paule P, Radu CS, Zeng W.
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