77 research outputs found
Counting subspaces of a finite vector space
In this expository article, we discuss the relation between the Gaussian
binomial and multinomial coefficients and ordinary binomial and multinomial
coefficients from a combinatorial viewpoint, based on expositions by Butler,
Knuth and Stanley.Comment: 15 pages, 3 figures, corrected versio
Reduction theory for a rational function field
Let be a split reductive group over a finite field \Fq. Let F=\Fq(t)
and let \A denote the ad\`eles of . We show that every double coset in
G(F)\bsl G(\A)/ K has a representative in a maximal split torus of . Here
is the set of integral ad\`elic points of . When ranges over general
linear groups this is equivalent to the assertion that any algebraic vector
bundle over the projective line is isomorphic to a direct sum of line bundles.Comment: 10 page
- …