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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper, we enumerate two families of pattern-avoiding permutations: those avoiding the vincular pattern $2underbracket{41}3$, which we call semi-Baxter permutations, and those avoiding the vincular patterns $2underbracket{41}3$, $3underbracket{14}2,$ and $3underbracket{41}2$, which we call strong-Baxter permutations. We call semi-Baxter numbers and strong-Baxter numbers the associated enumeration sequences. We prove that the semi-Baxter numbers enumerate in addition plane permutations (avoiding $2underbracket{14}3$). The problem of counting these permutations was open and has given rise to several conjectures, which we also prove in this paper. For each family (that of semi-Baxter---or, equivalently, plane---and that of strong-Baxter permutations), we describe a generating tree, which translates into a functional equation for the generating function. For semi-Baxter permutations, it is solved using (a variant of) the kernel method: this gives an expression for the generating function while als...

Semi-Baxter and Strong-Baxter: Two Relatives of the Baxter Sequence