For a comparison based sorting algorithm, it is desirable to:Be stableRun in $O(n\ \log n)$Operate in $O(1)$ spaceI 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?
Optimal comparison-based stable sorting in constant space
ds.algorithms;sorting
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.