Optimal comparison-based stable sorting in constant space For a comparison based sorting algorithm, it is desirable to:


Be stable
Run in $O(n\ \log n)$
Operate in $O(1)$ space


I can find algorithms that satisfy any two of these but I can't find any that satisfy all three. Does it exist? Is it proven not to exist?
Mergesort satisfies all three requirements (when merging is performed in place).
See Pardo, L.T., "Stable  sorting  and  merging  with  optimal  space  and  time 
bounds", SIAM J. Comput. 6 (1977), 351-372.