I have just pushed a new version of my partition tuple patch #13072 to the 
combinat queue which addresses the deprecation issues flagged by Nicolas 
and others. As there are many functions involved I thought I should post a 
summary of the functions affected so that the few people in the universe 
who care can check to see whether what I have done is sensible. 

The list below is in order of what I think is decreasing controversy.

   1. A=sage.combinat.partition.number_of_partitions() is marked for 
   deprecation in favour of B=sage.combinat.partitions.number_of_partitions(), 
   which is what function A() calls most of the time. As agreed above, 
   number_of_partitions() will stay in the global name space, but this made 
   the deprecation somewhat fiddly as I did not want to deprecate 
   number_of_partitions() for "normal use" because from the user perspective 
   this function will not change. Instead, I have deprecated the individual 
   options of number_of_partitions() so deprecation warnings are only 
   generated when A() does NOT call B(). In the global namespace, 
   number_of_partitions still points to A(). When the functions which are 
   marked for deprecation below are removed, number_of_partitions() should be 
   changed to point to B() and A() should be changed into a 
   deprecated_function_alias to B(). See the patch for more details.
   
   2. For use in Partitions().random_element() the function 
   number_of_partitions() was cached. This cached function was almost never 
   used so, assuming that caching this function is a good idea, I decided to 
   cache sage.combinat.partitions.number_of_partitions() always. Please let 
   me know if this is a bad idea.
   
   3. The two functions
   - cyclic_permutations_of_partition
      - cyclic_permutations_of_partition_iterator
   are deprecated in sage.combinat.partition and they have been moved to 
   sage.combinat.set_partition and renamed ...._of_set_partition... As far 
   as I can tell these functions are never used but, in any case, they are 
   methods on set partitions rather than partitions. Nonetheless, they need to 
   be deprecated from the global name space.
   
   4. The following functions were marked for deprecation several years ago 
   so they have been removed from sage.combinat.partition.py:
   - RestrictedPartitions
      - partitions_list
      - number_of_partitions_list
      - partitions_restricted
      - number_of_partitions_restricted
      
      5. The following functions now give deprecation warnings and are 
   marked for removal from the global name space:
   - partitions_set
      - number_of_partitions_set
      - ordered_partitions
      - number_of_ordered_partitions
      - partitions,
      - ferrers_diagram
      - partitions_greatest
      - partitions_greatest_eq
      - partitions_tuples
      - number_of_partitions_tuples
      - partition_power
   In all cases, these function are deprecated in favour of (methods in) 
   parent classes.

I also removed Nicolas' temporary patch 
trac_13072-tuples-of-partitions_number_of_partitions-nt.patch<http://combinat.sagemath.org/patches/rev/63e7c7e0183d>from
 the queue.

Andrew

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