赤毛のエイリークのサガ
The "Hervarar saga" from the 13th century tells that Eysteinn Beli was killed by Björn and his brothers as told in "Ragnar Lodbrok's saga", and they conquered all of Sweden. When Ragnar died Björn Ironside inherited Sweden. He had two sons, Refil and Erik Björnsson, who became the next king of Sweden. According to the "Saga of Erik the Red", Björn had a son named Asleik (Aslak), who was the ancestor of Thorfinn Karlsefni.