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Branden's Conjectures on the Boros-Moll Polynomials
Boros-Moll Polynomials Real-rootedness Sturm sequence 3-log-concavity
2014/6/3
We prove two conjectures of Brändén on the real-rootedness of polynomials Qn(x) and Rn(x) which are related to the Boros-Moll polynomials Pn(x). In fact, we show that both Qn(x) and Rn(x) form St...
The Boros-Moll polynomials Pm(a) arise in the evaluation of a quartic integral. It has been conjectured by Boros and Moll that these polynomials are infinitely log-concave. In this paper, we show that...
Partially 2-Colored Permutations and the Boros-Moll Polynomials
partially 2-colored permutation Boros-Moll polynomial rising factorial logconcavity bijection
2014/6/3
We find a combinatorial setting for the coefficients of the Boros-Moll polynomials Pm(a) in terms of partially 2-colored permutations. Using this model, we give a combinatorial proof of a recurrence r...
Branden's Conjectures on the Boros-Moll Polynomials
Boros-Moll Polynomials Real-rootedness Sturm sequence, 3-log-concavity
2012/5/24
We prove two conjectures of Br\"{a}nd\'{e}n on the real-rootedness of polynomials $Q_n(x)$ and $R_n(x)$ which are related to the Boros-Moll polynomials $P_n(x)$. In fact, we show that both $Q_n(x)$ an...
The Interlacing Log-concavity of the Boros-Moll Polynomials
interlacing log-concavity log-concavity the Boros-Moll polynomials
2014/6/3
We introduce the notion of interlacing log-concavity of a polynomial sequence {Pm(x)}m≥0, where Pm(x) is a polynomial of degree m with positive coefficients. This sequence is said to be interlacingly ...
On the Combinatorics of the Boros-Moll Polynomials
Jacobi polynomials Boros-Moll polynomials reluctant function Meixner endofunction bi-colored permutation
2014/6/3
The Boros-Moll polynomials arise in the evaluation of a quartic integral. The original double summation formula does not imply the fact that the coefficients of these polynomials are positive. Boros a...
The Reverse Ultra Log-Concavity of the Boros-Moll Polynomials
log-concavity reverse ultra log-concavity Boros-Moll polynomials
2014/6/3
We prove the reverse ultra log-concavity of the Boros-Moll polynomials. We further establish an inequality which implies the log-concavity of the sequence {i!di(m)} for any m ≥ 2, where di(m) are the ...
The Ratio Monotonicity of the Boros-Moll Polynomials
ratio monotone property spiral property unimodality log-concavity Jacobi polynomials Boros-Moll polynomials
2014/6/3
In their study of a quartic integral, Boros and Moll discovered a special class of Jacobi polynomials, which we call the Boros-Moll polynomials. Kauers and Paule proved the conjecture of Moll that the...