Cambrian trees are oriented and labeled trees which fulfill local conditions around each
node generalizing the classical conditions for binary search trees. Similar to binary trees for …

In data science, one is often confronted with a time series representing measurements of
some quantity of interest. Usually, in a first step, features of the time series need to be …

We introduce permutrees, a unified model for permutations, binary trees, Cambrian trees
and binary sequences. On the combinatorial side, we study the rotation lattices on …

Abstract The Malvenuto–Reutenauer algebra is a well-studied combinatorial Hopf algebra
with a basis indexed by permutations. This algebra contains a wide variety of interesting sub …

We define a two-parameter deformation of the quasi-shuffle by means of the formal group
law associated with the exponential generating function of the homogeneous Eulerian …

We explore the algebraic properties of a generalized version of the iterated-sums signature,
inspired by previous work of F. Király and H. Oberhauser. In particular, we show how to …

We develop the homology theory of the algebra of a regular semigroup, which is a
particularly nice case of a quasi-hereditary algebra in good characteristic. Directedness is …

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 …

We show that there exist two natural endomorphism algebras for shuffle bialgebras such as
Sh (X), where X is a graded set. One of these endomorphism algebras is a natural extension …

Noncrossing arc diagrams are combinatorial models for the equivalence classes of the
lattice congruences of the weak order on permutations. In this paper, we provide a general …