English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

The polynomial method has been used recently to obtain many striking resultsin combinatorial geometry. In this paper, we use affine Hilbert functions toobtain an estimation theorem in finite field geometry. The most natural way tostate the theorem is via a sort of bounded degree Zariski closure operation:given a set, we consider all polynomials of some bounded degree vanishing onthat set, and then the common zeros of these polynomials. For example, thedegree d closure of d + 1 points on a line will contain the whole line, as anypolynomial of degree at most d vanishing on the d + 1 points must vanish on theline. Our result is a bound on the size of a finite degree closure of a givenset. Finally, we adapt our use of Hilbert functions to the method ofmultiplicities.

Hilbert Functions and the Finite Degree Zariski Closure in Finite Field Combinatorial Geometry