Geodesic
Schur polynomials, banded Toeplitz matrices and widom's formula
Per Alexandersson1
1Department of Mathematics Stockholm University S-10691, Stockholm, Sweden
The electronic journal of combinatorics, Tome 19 (2012) no. 4
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We prove that for arbitrary partitions $\mathbf{\lambda} \subseteq \mathbf{\kappa},$ and integers $0\leq c the sequence of Schur polynomials $S_{(\mathbf{\kappa} + k\cdot\mathbf{1}^c)/(\mathbf{\lambda} + k\cdot\mathbf{1}^r)}(x_1,\dots,x_n)$ 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.
DOI : 10.37236/2651
Classification : 05E05, 05E10, 11C20, 15A18, 47B06
Mots-clés : banded Toeplitz matrices, Schur polynomials, widom/s determinant formula, sequence insertion, Young tableaux, recurrence

Per Alexandersson  1

1 Department of Mathematics Stockholm University S-10691, Stockholm, Sweden 
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     author = {Per Alexandersson},
     title = {Schur polynomials, banded {Toeplitz} matrices and widom's formula},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {4},
     doi = {10.37236/2651},
     zbl = {1267.05289},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2651/}
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Per Alexandersson. Schur polynomials, banded Toeplitz matrices and widom's formula. The electronic journal of combinatorics, Tome 19 (2012) no. 4. doi: 10.37236/2651

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