Smallest common denominators for the homogeneous components of the Baker-Campbell-Hausdorff series

Abstract

In a recent paper the author derived a formula for calculating common denominators for the homogeneous components of the Baker-Campbell-Hausdorff (BCH) series. In the present work it is proved that this formula actually yields the smallest such common denominators. In an appendix a new efficient algorithm for computing coefficients of the BCH series is presented, which is based on these common denominators, and requires only integer arithmetic rather than less efficient rational arithmetic.