@article{1981-knuth-transpose ,note={Note: reprinted in \cite[chapter 31]{2000-knuth-analysis}} ,author={Donald E. Knuth and Christos H. Papadimitriou} ,ISSN={0252--9742} ,journal={Bulletin of the European Association for Theoretical Computer Science} ,pages={2--4} ,title={{Duality in addition chains}} ,volume={13} ,year={1981} }