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

We show the power of Bruno Buchberger's seminal Groebner Basis algorithm,interfaced, seamlessly, with what we call symbolic dynamical programming, toautomatically generate algebraic equations satisfied by the generatingfunctions enumerating so-called Generalized Dyck Walks, i.e. 2D walks thatstart and end on the x-axis, and never dip below it, for an arbitrary set ofsteps. More impressively, we combine it with calculus (that Maple knows verywell!), to automatically compute generating functions for the sum-of-the-areasof these generalized Dyck paths, and even for the sum of any given power of theareas, enabling us to get statistical information about the area under a randomgeneralized Dyck path.

Using Symbolic Computation to Explore Generalized Dyck Paths and Their Areas