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

Graphical parking functions, or $G$-parking functions, are a generalizationof classical parking functions which depend on a connected multigraph $G$having a distinguished root vertex. Gaydarov and Hopkins characterized therelationship between $G$-parking functions and another vector-dependentgeneralization of parking functions, the $\boldsymbol{u}$-parking functions.The crucial component of their result was their classification of all graphs$G$ whose $G$-parking functions are invariant under action by the symmetricgroup $\mathfrak{S}_n$, where $n+1$ is the order of $G$. In this work, wepresent a 2-dimensional analogue of Gaydarov and Hopkins' results bycharacterizing the overlap between $G$-parking functions and 2-dimensional$\boldsymbol{U}$-parking functions, i.e., pairs of integer sequences whoseorder statistics are bounded by certain weights along lattice paths in theplane. Our key result is a total classification of all $G$ whose set of$G$-parking functions is $(\mathfrak{S}_p \times \mathfrak{S}_q)$-invariant,where $p+q+1$ is the order of $G$.

($\mathfrak{S}_p \times \mathfrak{S}_q$)-Invariant Graphical Parking Functions