The nth-order determinant of a Toeplitz-Hessenberg matrix is expressed as a sum over the integer partitions of n. Many combinatorial identities involving integer partitions and multinomial coefficients can be generated using this formula.
@article{bwmeta1.element.doi-10_2478_spma-2013-0003, author = {Mircea Merca}, title = {A note on the determinant of a Toeplitz-Hessenberg matrix}, journal = {Special Matrices}, volume = {1}, year = {2013}, pages = {10-16}, zbl = {1291.15015}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_spma-2013-0003} }
Mircea Merca. A note on the determinant of a Toeplitz-Hessenberg matrix. Special Matrices, Tome 1 (2013) pp. 10-16. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_spma-2013-0003/
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