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

For the one dimensional infinite group relaxation, we construct a sequence ofextreme valid functions that are piecewise linear and such that for everynatural number $k\geq 2$, there is a function in the sequence with $k$ slopes.This settles an open question in this area regarding a universal bound on thenumber of slopes for extreme functions. The function which is the pointwiselimit of this sequence is an extreme valid function that is continuous and hasan infinite number of slopes. This provides a new and more refinedcounterexample to an old conjecture of Gomory and Johnson stating that allextreme functions are piecewise linear. These constructions are extended toobtain functions for the higher dimensional group problems via thesequential-merge operation of Dey and Richard.

Extreme functions with an arbitrary number of slopes