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== Words (there is more to look at here) ==
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== Combinatorial* (not considered very carefully) ==
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 * Compositions has no option for allowing '0' parts (which are often useful)
 
 * 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 (Being worked on by JRB) ==
 * DyckWords? does not define Dyck words (done)
 * DyckWord.b_statistic() is not explained (done)
 * DyckWord.height() is not explained (done)
 * DyckWord.peaks() is not explained (done, BUT: sage's definition is *not* Haglund's definition. what is this function for?
 * 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
 * Actually calling MultichooseNK(3,2) returns a scary error message (probably due to a problem in CombinatorialClass)
== Tuples ==
 * This has very similar functionality to Combinations and MultichooseNK. These names should be made more consistent somehow.
== Necklaces ==
 * Necklaces? does not define necklaces
== Partitions ==
 * Perhaps a PartitionsOptions Class could be added where one could specify: French vs. English, maybe Dominance vs. Lex(?), others? The PermutationsOptions class is a good idea!
 * 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()
 * There should exist p.content(i,j) or p.content([i,j]) := j -i
 * 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() should accept p.hook(i,j) or p.hook([i,j])
 * 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()
== SkewPartitions ==
 * Commonalities with Partitions should be factored out! (hook lengths, for one example)
== Permutations ==
 * Permutations doc should define Bruhat order and recoils
 * Permutation doc should reference PermutationOptions
 * 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.action? could mention that to_permutation_group() allows for an action on polynomials
 * p.bruhat_* :
  1. greater/smaller return comb. classes, inversions,pred,succ return lists, *_iterator return iterators. Can this be made more consistent?
  1. Bruhat order should be defined or referenced in all of these
 * p.permutahedron_* :
  1. These all return lists (except for lequal() which is ok). Compare with bruhat above
  1. Left and right permutahedron order should be defined or referenced in all of these
 * p.charge() and p.cocharge() need to be implemented, p.ascents() would also possibly be useful
 * Typo in p.cycle_type? (non-increasing -> non-decreasing)
 * p.descents_composition? needs a definition of descent and an explanation of how to get the comp.
 * p.has_pattern() is redundant with p.avoids?
 * p.isignature, p.iswitch, p.iflip deserve references to Assaf.
 * p.iswitch? should mention that these are the dual knuth relations
 * the (non-dual) knuth relations should be implemented, as well as the boolean p.knuth_equivalent(q)
 * p.left_tableau? says it returns the right tableaux (but it's lying)
 * the only example for p.left_tableau() and p.right_tableau() is an involution; thus they are not distinguished
 * p.left_tableau? and p.right_tableau? should provide a specific reference to the algorithm
 * p.longest_increasing_subsequence() should be called p.longest_increasing_subsequences() (plural)
 * p.major_index? typo: "add one the number of" -> "add one to each of"
 * p.number_of_descents? should define descent and explain the final_descents option
 * p.number_of_idescents? should include the word 'inverse' and explain final_descents
 * p.number_of_recoils? should define recoil
 * p.number_of_saliances? should define saliances
 * p.recoils_composition? needs a definition of recoil and an explanation of how to get the comp.
 * p.reduced_word() implies there is only one. Is the point that it is faster than p.reduced_word_lexmin() ?
 * p.reduced_word* should all define or reference reduced words in the doc
 * p.remove_extra_fixed_points() should be called p.remove_trailing_fixed_points(). When applied to [1] it should return []
 * p.robinson_schensted? should provide a specific reference to the algorithm
 * p.runs? should define runs... the definition is quite short
 * p.signature? should define signature
 * p.to_*
  1. is the 'to' needed in the name? ex: p.to_cycles() could be called p.cycles() to be compatible with p.cycle_string()
  1. lehmer_code? and lehmer_cocode? should be defined
  1. tableau_by_shape? should emphasize that it simply fills the given shape with p in reading order--no col-strict condition is enforced
  1. permutation_group_element should emphasize that this can be used to act on polynomials
 * Perhaps p.excedences() would be useful, as well as p.weak_excedences()
== PermutationGroup* ==
 * Not generally considered (i'm exhausted on permutations) but is it possible for PermutationGroupElement to be merged with Permutation?
== q_analogues.py ==
 * These are extremely useful and should be generally available
 * q_pochhammer or q-series = (a;q)_n := \prod_{k=0}^{n-1} (1 - aq^k) should be implemented.
== SetPartitions* ==
 * Are all the names SetPartitions*k necessary in the global namespace?
== Tableau ==
 * The following are for t a Tableau
 * t.major_index is not what most people call the major index of a tableaux. This should be called dmaj.
 * There should be a general method for adding a row or a cell, or changing a cell
 * All the katabolism stuff needs better doc
 * t.katabolism_sequence() gives an infinite loop if t is the empty tableau
== More to come... ==

This is a great page. There is lots of weirdness in the combinatorics stuff, and we should really clean it up. I can start working on the simpler stuff here next week. --DanDrake

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)

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 (Being worked on by JRB)

  • DyckWords? does not define Dyck words (done)

  • DyckWord.b_statistic() is not explained (done)

  • DyckWord.height() is not explained (done)

  • DyckWord.peaks() is not explained (done, BUT: sage's definition is *not* Haglund's definition. what is this function for?

  • 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

Lyndon Words

MultichooseNK

  • MultichooseNK has no useful documentation
  • The name MultichooseNK does not compare well with Combinations, though they do very similar things
  • Actually calling MultichooseNK(3,2) returns a scary error message (probably due to a problem in CombinatorialClass)

Tuples

  • This has very similar functionality to Combinations and MultichooseNK. These names should be made more consistent somehow.

Necklaces

  • Necklaces? does not define necklaces

Partitions

  • Perhaps a PartitionsOptions Class could be added where one could specify: French vs. English, maybe Dominance vs. Lex(?), others? The PermutationsOptions class is a good idea!

  • 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()
  • There should exist p.content(i,j) or p.content([i,j]) := j -i
  • 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() should accept p.hook(i,j) or p.hook([i,j])
  • 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()

SkewPartitions

  • Commonalities with Partitions should be factored out! (hook lengths, for one example)

Permutations

  • Permutations doc should define Bruhat order and recoils
  • Permutation doc should reference PermutationOptions

  • 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.action? could mention that to_permutation_group() allows for an action on polynomials
  • 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
  • p.permutahedron_* :
    1. These all return lists (except for lequal() which is ok). Compare with bruhat above
    2. Left and right permutahedron order should be defined or referenced in all of these
  • p.charge() and p.cocharge() need to be implemented, p.ascents() would also possibly be useful
  • Typo in p.cycle_type? (non-increasing -> non-decreasing)

  • p.descents_composition? needs a definition of descent and an explanation of how to get the comp.
  • p.has_pattern() is redundant with p.avoids?
  • p.isignature, p.iswitch, p.iflip deserve references to Assaf.
  • p.iswitch? should mention that these are the dual knuth relations
  • the (non-dual) knuth relations should be implemented, as well as the boolean p.knuth_equivalent(q)
  • p.left_tableau? says it returns the right tableaux (but it's lying)
  • the only example for p.left_tableau() and p.right_tableau() is an involution; thus they are not distinguished
  • p.left_tableau? and p.right_tableau? should provide a specific reference to the algorithm
  • p.longest_increasing_subsequence() should be called p.longest_increasing_subsequences() (plural)
  • p.major_index? typo: "add one the number of" -> "add one to each of"

  • p.number_of_descents? should define descent and explain the final_descents option
  • p.number_of_idescents? should include the word 'inverse' and explain final_descents
  • p.number_of_recoils? should define recoil
  • p.number_of_saliances? should define saliances
  • p.recoils_composition? needs a definition of recoil and an explanation of how to get the comp.
  • p.reduced_word() implies there is only one. Is the point that it is faster than p.reduced_word_lexmin() ?
  • p.reduced_word* should all define or reference reduced words in the doc
  • p.remove_extra_fixed_points() should be called p.remove_trailing_fixed_points(). When applied to [1] it should return []
  • p.robinson_schensted? should provide a specific reference to the algorithm
  • p.runs? should define runs... the definition is quite short
  • p.signature? should define signature
  • p.to_*
    1. is the 'to' needed in the name? ex: p.to_cycles() could be called p.cycles() to be compatible with p.cycle_string()
    2. lehmer_code? and lehmer_cocode? should be defined
    3. tableau_by_shape? should emphasize that it simply fills the given shape with p in reading order--no col-strict condition is enforced
    4. permutation_group_element should emphasize that this can be used to act on polynomials
  • Perhaps p.excedences() would be useful, as well as p.weak_excedences()

PermutationGroup*

  • Not generally considered (i'm exhausted on permutations) but is it possible for PermutationGroupElement to be merged with Permutation?

q_analogues.py

  • These are extremely useful and should be generally available
  • q_pochhammer or q-series = (a;q)_n := \prod_{k=0}{n-1} (1 - aqk) should be implemented.

SetPartitions*

  • Are all the names SetPartitions*k necessary in the global namespace?

Tableau

  • The following are for t a Tableau
  • t.major_index is not what most people call the major index of a tableaux. This should be called dmaj.
  • There should be a general method for adding a row or a cell, or changing a cell
  • All the katabolism stuff needs better doc
  • t.katabolism_sequence() gives an infinite loop if t is the empty tableau

More to come...

This is a great page. There is lots of weirdness in the combinatorics stuff, and we should really clean it up. I can start working on the simpler stuff here next week. --DanDrake

combinat/Weirdness (last edited 2018-11-06 19:45:34 by chapoton)