title: On a Nesbitt - Carlitz determinant
metadata.name: dc.contributor.author
metadata.value: Pimenov, Kostantin I.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-04-10T12:48:41Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-04-10T12:48:41Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Pimenov K. I. On a Nesbitt - Carlitz determinant. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 1, pp. 85–90.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2020.109
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17331
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: A matrix whose component are binomial coefficients and determinant was calculated earlier
  by L. Carlitz is investigated. It is shown that Carlitz matrix is the result of binomal
  specialization for dual Jacobi Trudi determinant presentation of certain Schur function. It leads to another way to calculate Carlitz determinant based upon symmetric function
  theory. The eigenvalues of Carlitz matrix are shown to be powers of two as well. In order to
  calculate these eigenvalues the author uses suitable linear operator on the space of polynomials
  whose degree does not exceed given number. It is shown that in suitable basis matrix
  of that linear operator has triangular form with powers of two on its diagonal. Main result
  is generalised from quadratic to cubic case corresponding to a certain matrix, consisted of
  trinomial coefficients.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work is supported by Russian Foundation for Basic Research (grant N16-01-00750).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: linear algebra
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: binomial coefficients
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: symmetric functions
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: matrix eigenvalues
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On a Nesbitt - Carlitz determinant
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 85-90.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17331/1/85-90.pdf
resources.format: Adobe PDF
resources.size: 270,27 kB