AN ALGEBRAIC INTERPRETATION OF THE q-BINOMIAL COEFFICIENTS

Yıl 2009, Cilt: 6 Sayı: 6, 23 - 30, 01.12.2009

Michael Braun

Öz

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.

Anahtar Kelimeler

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