Opened 3 years ago
Closed 3 years ago
#22105 closed enhancement (fixed)
Implement ksplit basis for kBoundedSubspace of symmetric functions
Reported by:  zabrocki  Owned by:  

Priority:  major  Milestone:  sage7.6 
Component:  combinatorics  Keywords:  combinat, sf 
Cc:  aschilling  Merged in:  
Authors:  Mike Zabrocki  Reviewers:  Anne Schilling 
Report Upstream:  N/A  Work issues:  
Branch:  011ff3f (Commits)  Commit:  011ff3f4b20c0dede74a88b92ffbfc1ddd12c5ef 
Dependencies:  Stopgaps: 
Description (last modified by )
The ksplit basis of the subspace of symmetric functions is defined using the HallLittlewood creation operators. If lambda = mu + nu
where lambda
, mu
and nu
are lists representing k
bounded partitions and mu
has largest hook equal to k
, then ksplit(nu).hl_creation_operator(mu) == ksplit(lambda)
.
This ticket implements the ksplit functions as a basis of the kBoundedSubspace
. It is accessed from the symmetric functions either by
sage: SymmetricFunctions(QQ['t'].fraction_field()).kBoundedSubspace(3).ksplit() 3bounded Symmetric Functions over Fraction Field of Univariate Polynomial Ring in t over Rational Field in the 3split basis
or by the shortcut
sage: SymmetricFunctions(QQ['t'].fraction_field()).ksplit(3)
In either case, the value of t
is specified as an optional argument whenever k
is specified and the default value of this argument is 't'
which needs to be an element of the ring if it is not specified.
A few minor changes are made to the other kBoundedSubspace
bases (addition of a shortcut to access k
and t
in the basis, a minor change in the full name of the kSchur basis to make it more consistent).
Change History (7)
comment:1 Changed 3 years ago by
 Description modified (diff)
 Status changed from new to needs_review
comment:2 Changed 3 years ago by
 Reviewers set to Anne Schilling
 Status changed from needs_review to positive_review
comment:3 Changed 3 years ago by
 Commit changed from 06edc02d8bb9bdf77be51617fbe112a4f05a85fa to 011ff3f4b20c0dede74a88b92ffbfc1ddd12c5ef
 Status changed from positive_review to needs_review
Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:
011ff3f  missing double colon in sf.py

comment:4 Changed 3 years ago by
Sorry about that. I was reviewing the html doc strings and noticed this missing ::
comment:5 Changed 3 years ago by
 Status changed from needs_review to positive_review
comment:6 Changed 3 years ago by
 Milestone changed from sage7.5 to sage7.6
comment:7 Changed 3 years ago by
 Branch changed from public/sf/ksplit to 011ff3f4b20c0dede74a88b92ffbfc1ddd12c5ef
 Resolution set to fixed
 Status changed from positive_review to closed
Looks great! Thank you, Mike, for implementing this! I ran the tests and also tested the code on some examples. It seems to work as desired.