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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Building off recent work of Garg and Peng, we continue the investigation intoclassical and consecutive pattern avoidance in rooted forests, resolving someof their conjectures and questions and proving generalizations wheneverpossible. Through extensions of the forest Simion-Schmidt bijection introducedby Anders and Archer, we demonstrate a new family of forest-Wilf equivalences,completing the classification of forest-Wilf equivalence classes for setsconsisting of a pattern of length 3 and a pattern of length at most $5$. Wealso find a new family of nontrivial c-forest-Wilf equivalences between singlepatterns using the forest analogue of the Goulden-Jackson cluster method,showing that a $(1-o(1))^n$-fraction of patterns of length $n$ satisfy anontrivial c-forest-Wilf equivalence and that there are c-forest-Wilfequivalence classes of patterns of length $n$ of exponential size.Additionally, we consider a forest analogue of super-strong-c-Wilf equivalence,introduced for permutations by Dwyer and Elizalde, showing thatsuper-strong-c-forest-Wilf equivalences are trivial by enumerating linearextensions of forest cluster posets.

Wilf Equivalences for Patterns in Rooted Labeled Forests