Schur polynomials, banded Toeplitz matrices and Widom's formula
2012 (English)In: The Electronic Journal of Combinatorics, ISSN 1077-8926, Vol. 19, no 4, P22- p.Article in journal (Refereed) Published
We prove that for arbitrary partitions lambda subset of kappa, and integers 0 <= c < r <= n, the sequence of Schur polynomials S(kappa+k.1c)/(lambda+k.1r)(x(1), ... , x(n)) for k sufficiently large, satisfy a linear recurrence. The roots of the characteristic equation are given explicitly. These recurrences are also valid for certain sequences of minors of banded Toeplitz matrices. In addition, we show that Widom's determinant formula from 1958 is a special case of a well-known identity for Schur polynomials.
Place, publisher, year, edition, pages
2012. Vol. 19, no 4, P22- p.
Banded Toeplitz matrices, Schur polynomials, Widom's determinant formula, sequence insertion, Young tableaux, recurrence
Research subject Mathematics
IdentifiersURN: urn:nbn:se:su:diva-83811ISI: 000310833500004OAI: oai:DiVA.org:su-83811DiVA: diva2:577130