Remark on the formula by Rakhmanov and Steklov's conjecture

A Remark about Mahler’s Conjecture and the Maximum Value of Box Splines

In this paper, we recast a special case of Mahler’c conjecture by the maximum value of box splines. This is the case of polytopes with at most 2n + 2 facets. An asymptotic formula for univariate box splines is given. Based on the formula, Mahler’s conjecture is proved in this case provided n is big enough.

On a Conjecture of E.a. Rakhmanov

It is shown that a conjecture of E.A. Rakhmanov is true concerning the zero distribution of orthogonal polynomials with respect to a measure having a discrete real support. We also discuss the case of extremal polynomials with respect to some discrete L p {norm, 0 < p 1, and give an extension to complex supports. Furthermore, we present properties of weighted Fekete points with respect to discr...

On Schur parameters in Steklov's problem

We study the recursion (aka Schur) parameters for monic polynomials orthogonal on the unit circle with respect to a weight which provides negative answer to the conjecture of Steklov.

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Towards a Human Proof of Gessel’s Conjecture

We interpret walks in the first quadrant with steps {(1, 1), (1, 0), (−1, 0), (−1,−1)} as a generalization of Dyck words with two sets of letters. Using this language, we give a formal expression for the number of walks using the steps above, beginning and ending at the origin. We give an explicit formula for a restricted class of such words using a correspondence between such words and Dyck pa...