Lattice Path Proofs of Extended Bressoud-Wei and Koike Skew Schur Function Identities

Hamel, Angèle M.; King, Ronald C.

doi:10.37236/534

Electron. J. Combin.

2011

DOI: 10.37236/534

|View full text |Cite

Lattice Path Proofs of Extended Bressoud-Wei and Koike Skew Schur Function Identities

Angèle M. Hamel¹,

Ronald C. King²

Abstract: A recent paper of the present authors provides extensions to two classical determinantal results of Bressoud and Wei, and of Koike. The proofs in that paper were algebraic. The present paper contains combinatorial lattice path proofs.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2011

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Extended Bressoud–Wei and Koike skew Schur function identities

Hamel

King

2011

Journal of Combinatorial Theory, Series A

View full text Add to dashboard Cite

The Jacobi-Trudi identity expresses a skew Schur function as a determinant of complete symmetric functions. Bressoud and Wei extend this idea, introducing an integer parameter t −1 and showing that signed sums of skew Schur functions of a certain shape are expressible once again as a determinant of complete symmetric functions. Koike provides a Jacobi-Trudi-style definition of universal rational characters of the general linear group and gives their expansion as a signed sum of products of Schur functions in two distinct sets of variables. Here we extend Bressoud and Wei's formula by including an additional parameter and extending the result to the case of all integer t. Then we introduce this parameter idea to the Koike formula, extending it in the same way. We prove our results algebraically using Laplace determinantal expansions.

show abstract

Extended Bressoud–Wei and Koike skew Schur function identities

Hamel

King

2011

Journal of Combinatorial Theory, Series A

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Lattice Path Proofs of Extended Bressoud-Wei and Koike Skew Schur Function Identities

Abstract: A recent paper of the present authors provides extensions to two classical determinantal results of Bressoud and Wei, and of Koike. The proofs in that paper were algebraic. The present paper contains combinatorial lattice path proofs.

Cited by 1 publication

References 10 publications

Extended Bressoud–Wei and Koike skew Schur function identities

Extended Bressoud–Wei and Koike skew Schur function identities

Contact Info

Product

Resources

About