Weirdness

Words (there is more to look at here)

• sage.combinat.word is not imported by default
• word.symmetric_group_action_on_values does not naturally belong in word
• word.standard should be called word.standardization
• word.charge returns the cocharge

Combinatorial* (not considered very carefully)

• CombinatorialAlgebra has no useful documentation

• CombinatorialClass has no documentation

• It would be nice for CombinatorialObject to have a method 'indices' which returns a list of the index of *every* occurrence of x

Combinations

• Looks good! (Just recording here that it was looked at).

Compositions

• Compositions has no option for allowing '0' parts (which are often useful) (IntegerVectors does this. There should be a pointer.)

• Composition will allow entries with '0' parts (but not, for example, negative parts). It's not clear that all methods make sense when '0' parts are allowed.
• Composition.conjugate() is not explained
• Composition.descents() is not explained
• Composition.major_index() doc-string says it is the sum of the descents. This is not true for the given example.
• Composition.refinement() is not explained

• SignedCompositions has no corresponding element class SignedComposition

Dyck Words

• DyckWords? does not define Dyck words

• DyckWord.b_statistic() is not explained

• DyckWord.height() is not explained

• DyckWord.peaks() is not explained

• DyckWord.to_noncrossing_partition() could use a better reference

• DyckWord.to_tableau is not explained

• DyckWord.to_* for * in {ordered_tree, triangulation} is not implemented. Warning: Implementing bijections between Catalan objects can be a never-ending task.

Integer Vectors

• IntegerVectors has no corresponding element class IntegerVector (or Word, etc.)

• WeightedIntegerVectors has no corresponding element class WeightedIntegerVector (or IntegerVector, or Word, etc.)

Lyndon Words

• LyndonWords has no corresponding element class LyndonWord (or Word, etc.)

• LyndonWords? does not define Lyndon words

MultichooseNK

• MultichooseNK has no useful documentation
• The name MultichooseNK does not compare well with Combinations, though they do very similar things

Necklaces

• Necklaces? does not define necklaces

Partitions

• PartitionsGreatestEQ, PartitionsGreatestLE, PartitionsInBox are redundant with options passed to Partitions

• The doc for Partition should point out that < compares lexicographically

• The doc for Partition says 'Sage uses the English convention...' this should be expanded and mention 0-indexing; in fact it should also mention that partitions can be interpreted as diagrams
• The partition* stuff is all redundant
• p.arm(i,j) and p.leg(i,j) should also be callable as p.arm([i,j]), p.leg([i,j])
• (For the following comments, let p be a partition)
• p.arm_lengths() and p.leg_lengths() should be called p.arm_length_tableau(), ...
• p.arm_legs_coeff() is not defined
• p.associated() is an alias for p.conjugate(). Is it necessary?
• p.atom() is not defined
• p.boxes() would be better called p.cells()
• An reference, definition, or at least an example should be given for the q,t-analog of p.centralizer_size()
• p.character_polynomial() deserves a reference
• p.dominate() should be called p.dominated_partitions() (or something more clear)
• p.down(), p.down_list(), p.up(), p.up_list() could have better names? (restrict/induce? is there a convention for a generator vs a list? is this too redundant?)
• is p.evaluation() a standard name?
• p.ferrers_diagram() is basically redundant with p.pp()
• p.generalized_pochhammer_symbol? needs a definition and, better, a reference
• p.hook_lengths() should be called p.hook_length_tableau()
• p.hook_polynomial() needs a definition and/or reference
• p.hook_product() needs a definition and/or reference, and the parameter should default to 1
• the following example blows up:

  sage: m = p.jacobi_trudi(); m.row(0)

• p.jacobi_trudi() should also include an option for the 'e' version
• p.k_atom() needs a definition or reference
• p.k_conjugate() could use a reference
• p.k_split() needs a definition or reference
• given p.outside_corners() should p.corners() be renamed?
• a function p.add_cell(i,j) (also taking p.add_cell([i,j])) is *really* needed
• p.pp() should be called p.pretty_print() or just p.print()
• p.r_core() and p.r_quotient() need defintions and/or references. Also should be called core and quotient
• p.reading_tableau() needs a definition
• p.remove_box() should be called p.remove_cell()
• p.remove_box(i,j) should understand p.remove_box([i,j])
• p.to_exp() needs a better name
• p.upper_hook() needs a definition or reference
• p.upper_hook_lengths() should be called p.upper_hook_length_tableau()

Permutations

• The keywords called 'recoils' in Permutations should perhaps be called 'ascents'
• The Permutation constructor does not check enough: Permutation([1,1,1]) and Permutation([-3,7]) don't break, for example
• For the following, let p be a Permutation
• p.bruhat_* :
  1. greater/smaller return comb. classes, inversions,pred,succ return lists, *_iterator return iterators. Can this be made more consistent?
  2. Bruhat order should be defined or referenced in all of these