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4 papers · 2 filters
The Hopf algebras of signed permutations, of weak quasi-symmetric functions and of Malvenuto-Reutenauer
Li Guo, Jean-Yves Thibon, Houyi Yu
This paper builds on two covering Hopf algebras of the Hopf algebra QSym of quasi-symmetric functions, with linear bases parameterized by compositions. One is the Malvenuto-Reutena…
Compacted binary trees admit a stretched exponential
Andrew Elvey Price, Wenjie Fang, Michael Wallner
A compacted binary tree is a directed acyclic graph encoding a binary tree in which common subtrees are factored and shared, such that they are represented only once. We show that…
The Steep-Bounce Zeta Map in Parabolic Cataland
Cesar Ceballos, Wenjie Fang, Henri Mühle
As a classical object, the Tamari lattice has many generalizations, including -Tamari lattices and parabolic Tamari lattices. In this article, we unify these generalizations in…
Tree series and pattern avoidance in syntax trees
Samuele Giraudo
A syntax tree is a planar rooted tree where internal nodes are labeled on a graded set of generators. There is a natural notion of occurrence of contiguous pattern in such trees. W…