Infinite Boolean polynomials I

Infinite Products of Cyclotomic Polynomials

We study analytic properties of certain infinite products of cyclotomic polynomials that generalize some introduced by Mahler. We characterize those that have the unit circle as a natural boundary and use associated Dirichlet series to obtain their asymptotic behavior near roots of unity.

Some Comments on Infinite Boolean Functions

Fast Gröbner Basis Computation for Boolean Polynomials

We introduce the Macaulay2 package BooleanGB, which computes a Gröbner basis for Boolean polynomials using a binary representation rather than symbolic. We compare the runtime of several Boolean models from systems in biology and give an application to Sudoku.

Kazhdan–Lusztig polynomials of boolean elements

We give closed combinatorial product formulas for Kazhdan–Lusztig poynomials and their parabolic analogue of type q in the case of boolean elements, introduced in [M. Marietti, Boolean elements in Kazhdan–Lusztig theory, J. Algebra 295 (2006)], in Coxeter groups whose Coxeter graph is a tree. Such formulas involve Catalan numbers and use a combinatorial interpretation of the Coxeter graph of th...

An Infinite Series of Kronecker Conjugate Polynomials

Let K be a field of characteristic 0, t a transcendental over K, and Γ be the absolute Galois group of K(t). Then two non-constant polynomials f, g ∈ K[X] are said to be Kronecker conjugate if an element of Γ fixes a root of f(X) − t if and only if it fixes a root of g(X) − t. If K is a number field, and f, g ∈ OK [X] where OK is the ring of integers of K, then f and g are Kronecker conjugate i...