Opened 3 years ago

Closed 3 years ago

#22105 closed enhancement (fixed)

Implement k-split basis for kBoundedSubspace of symmetric functions

Reported by: zabrocki Owned by:
Priority: major Milestone: sage-7.6
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 zabrocki)

The k-split basis of the subspace of symmetric functions is defined using the Hall-Littlewood 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()
3-bounded Symmetric Functions over Fraction Field of Univariate Polynomial Ring in t over Rational Field in the 3-split 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 k-Schur basis to make it more consistent).

Change History (7)

comment:1 Changed 3 years ago by zabrocki

  • Description modified (diff)
  • Status changed from new to needs_review

comment:2 Changed 3 years ago by aschilling

  • Authors changed from zabrocki to Mike Zabrocki
  • Reviewers set to Anne Schilling
  • Status changed from needs_review to positive_review

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.

comment:3 Changed 3 years ago by git

  • 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:

011ff3fmissing double colon in

comment:4 Changed 3 years ago by zabrocki

Sorry about that. I was reviewing the html doc strings and noticed this missing ::

comment:5 Changed 3 years ago by aschilling

  • Status changed from needs_review to positive_review

comment:6 Changed 3 years ago by chapoton

  • Milestone changed from sage-7.5 to sage-7.6

comment:7 Changed 3 years ago by vbraun

  • Branch changed from public/sf/ksplit to 011ff3f4b20c0dede74a88b92ffbfc1ddd12c5ef
  • Resolution set to fixed
  • Status changed from positive_review to closed
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