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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $I_n$ be the ideal of all algebraic relations on the slopes of the$\binom{n}{2}$ lines formed by placing $n$ points in a plane and connectingeach pair of points with a line. Under each of two natural term orders, theinitial ideal of $I_n$ is generated by monomials corresponding to permutationssatisfying a certain pattern-avoidance condition. We show bijectively thatthese permutations are enumerated by the updown (or Euler) numbers, therebyobtaining a formula for the number of generators of the initial ideal of $I_n$in each degree.

Updown numbers and the initial monomials of the slope variety