A combinatorial problem related to Mahler’s measure
نویسنده
چکیده
We give a generalization of a result of Myerson on the asymptotic behavior of norms of certain Gaussian periods. The proof exploits properties of the Mahler measure of a trinomial.
منابع مشابه
Polynomial Inequalities, Mahler’s Measure, and Multipliers
We survey polynomial inequalities obtained via coefficient multipliers, for norms defined by the contour or the area integrals over the unit disk. Special attention is devoted to the Szegő composition and the inequalities related to Mahler’s measure. We also consider a new height on polynomial spaces defined by the integral over the normalized area measure on the unit disk. This natural analog ...
متن کاملSelecting Efficient Service-providers in Electric Power Distribution Industry Using Combinatorial Reverse Auction
In this paper, a combinatorial reverse auction mechanism is proposed for selecting the most efficient service-providers for resolving sustained power interruptions in multiple regions of an electric power distribution company’s responsibility area. Through this mechanism, supplying the required service in each region is assigned to only one potential service-provider considering two criteria in...
متن کاملAuxiliary Polynomials for Some Problems regarding Mahler’s Measure
We describe an iterative method of constructing some favorable auxiliary polynomials used to obtain lower bounds in some problems of algebraic number theory. With this method we improve a lower bound on Mahler’s measure of a polynomial with no cyclotomic factors whose coefficients are all congruent to 1 modulo m for some integer m ≥ 2, raise a lower bound in the problem of Schinzel and Zassenha...
متن کاملThe Many Aspects of Mahler’s Measure
The idea behind the workshop was to bring together experts specializing in many different fields: dynamical systems, K-theory, number theory, topology, analysis, to explore some of the many apparently different ways that Mahler’s measure appears in different areas of Mathematics. The hope was to encourage cross-fertilization between these disciplines and increase our understanding of Mahler’s m...
متن کاملMahler’s Expansion and Boolean Functions
The substitution of X by X2 in binomial polynomials generates sequences of integers by Mahler’s expansion. We give some properties of these integers and a combinatorial interpretation with covers by projection. We also give applications to the classification of boolean functions. This sequence arose from our previous research on classification and complexity of Binary Decision Diagrams (BDD) as...
متن کامل