5 papers · 1 filter
Stoimenow matchings avoiding multiple Catalan patterns simultaneously
Shuzhen Lv, Sergey Kitaev
Motivated by Vassiliev's knot invariants, Stoimenow introduced a special class of matchings, now known as Stoimenow matchings. These matchings have since been linked to various com…
Catalan structures arising from pattern-avoiding Stoimenow matchings and other Fishburn objects
Shuzhen Lv, Sergey Kitaev, Philip B. Zhang
In connection with Vassiliev's knot invariants, Stoimenow introduced in 1998 a class of matchings, also known as regular linearized chord diagrams. These matchings are linked to va…
Joint equidistributions of mesh patterns 123 and 132 with minus antipodal shadings
Shuzhen Lv, Philip B. Zhang
The study of joint equidistributions of mesh patterns 123 and 132 with the same symmetric shadings was recently initiated by Kitaev and Lv, where 75 of 80 potential joint equidistr…
Joint equidistributions of mesh patterns 123 and 321 with symmetric and minus-antipodal shadings
Shuzhen Lv, Philip B. Zhang
In this paper, we extend recent results by Lv and Kitaev by proving 20 (out of 22 possible) joint equidistributions of mesh patterns 123 and 321 with symmetric shadings, as well as…
On (joint) equidistributions of mesh patterns 123 and 132 with symmetric shadings
Sergey Kitaev, Shuzhen Lv
A notable problem within permutation patterns that has attracted considerable attention in literature since 1973 is the search for a bijective proof demonstrating that 123-avoiding…