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AN ALGEBRAIC INTERPRETATION OF THE q-BINOMIAL COEFFICIENTS

Year 2009, Volume: 6 Issue: 6, 23 - 30, 01.12.2009

Michael Braun

Abstract

Gaussian numbers, also called Gaussian polynomials or q-binomial coefficients are the q-analogs of common binomial coefficients. First introduced by Euler these polynomials have played an important role in many different branches of mathematics. Sylvester discovered the unimodality of their coefficients, using invariant theory. Gauss recognized the connection of the coefficients to proper integer partitions using a combinatorial interpretation. Here in this paper we are going to point out a new algebraic interpretation of the Gaussian polynomials as orbits of the Borel group on subspaces.

Keywords

q-binomial coefficient Gauss number Gauss polynomial group action Borel group

Year 2009, Volume: 6 Issue: 6, 23 - 30, 01.12.2009

Michael Braun

Abstract

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Other ID JA44YA23MD
Authors

Michael Braun This is me

Publication Date December 1, 2009
Published in Issue Year 2009 Volume: 6 Issue: 6

Cite

APA Braun, M. (2009). AN ALGEBRAIC INTERPRETATION OF THE q-BINOMIAL COEFFICIENTS. International Electronic Journal of Algebra, 6(6), 23-30. https://izlik.org/JA54XC99YG
AMA 1.Braun M. AN ALGEBRAIC INTERPRETATION OF THE q-BINOMIAL COEFFICIENTS. IEJA. 2009;6(6):23-30. https://izlik.org/JA54XC99YG
Chicago Braun, Michael. 2009. “AN ALGEBRAIC INTERPRETATION OF THE Q-BINOMIAL COEFFICIENTS”. International Electronic Journal of Algebra 6 (6): 23-30. https://izlik.org/JA54XC99YG.
EndNote Braun M (December 1, 2009) AN ALGEBRAIC INTERPRETATION OF THE q-BINOMIAL COEFFICIENTS. International Electronic Journal of Algebra 6 6 23–30.
IEEE [1]M. Braun, “AN ALGEBRAIC INTERPRETATION OF THE q-BINOMIAL COEFFICIENTS”, IEJA, vol. 6, no. 6, pp. 23–30, Dec. 2009, [Online]. Available: https://izlik.org/JA54XC99YG
ISNAD Braun, Michael. “AN ALGEBRAIC INTERPRETATION OF THE Q-BINOMIAL COEFFICIENTS”. International Electronic Journal of Algebra 6/6 (December 1, 2009): 23-30. https://izlik.org/JA54XC99YG.
JAMA 1.Braun M. AN ALGEBRAIC INTERPRETATION OF THE q-BINOMIAL COEFFICIENTS. IEJA. 2009;6:23–30.
MLA Braun, Michael. “AN ALGEBRAIC INTERPRETATION OF THE Q-BINOMIAL COEFFICIENTS”. International Electronic Journal of Algebra, vol. 6, no. 6, Dec. 2009, pp. 23-30, https://izlik.org/JA54XC99YG.
Vancouver 1.Braun M. AN ALGEBRAIC INTERPRETATION OF THE q-BINOMIAL COEFFICIENTS. IEJA [Internet]. 2009 Dec. 1;6(6):23-30. Available from: https://izlik.org/JA54XC99YG