AN ALGEBRAIC INTERPRETATION OF THE q-BINOMIAL COEFFICIENTS

Michael Braun

EN

AN ALGEBRAIC INTERPRETATION OF THE q-BINOMIAL COEFFICIENTS

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

Details

Primary Language

English

Subjects

-

Journal Section

-

Authors

Michael Braun This is me

Publication Date

December 1, 2009

Submission Date

December 1, 2009

Acceptance Date

-

Published in Issue

Year 2009 Volume: 6 Number: 6

IZ

https://izlik.org/JA54XC99YG

Cite

RIS / Bibtex

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.Michael Braun. AN ALGEBRAIC INTERPRETATION OF THE q-BINOMIAL COEFFICIENTS. IEJA [Internet]. 2009 Dec. 1;6(6):23-30. Available from: https://izlik.org/JA54XC99YG