5 papers
Aldous-type Spectral Gaps in Unitary Groups
Gil Alon, Doron Puder
Aldous' spectral gap conjecture, proven by Caputo, Liggett and Richthammer, states the following: for any set of transpositions in the symmetric group , the spectr…
The Combinatorial Nullstellensatz, Chevalley-Warning Theorem and weak Finitesatz in skew polynomial rings
Gil Alon, Angelot Behajaina, Elad Paran
We study zeros of polynomials in the multivariate skew polynomial ring , where is an automorphism of a division ring . We prove a generalization of Nog…
On the geometry of zero sets of central quaternionic polynomials II
Gil Alon, Adam Chapman, Elad Paran
Following the work of the first and last authors [2], we further analyze the structure of a zero set of a left ideal in the ring of central polynomials over the quaternion algebra…
On the geometry of zero sets of central quaternionic polynomials
Gil Alon, Elad Paran
Let R be the ring of polynomials in n central variables over the real quaternion algebra H, and let I be a left ideal in R. We prove that if a polynomial p in R vanishes at all the…
On the stopping time of the Collatz map in
Gil Alon, Angelot Behajaina, Elad Paran
We study the stopping time of the Collatz map for a polynomial , and bound it by , improving upon the quadratic bound proven by Hicks…