Lattice Path Enumeration Page 1 Chapter 10 Lattice Path Enumeration Christian Krattenthaler
Universität Wien CONTENTS 10.1 Introduction ....................................................... 589 10.2 Lattice …

The “classical” parking functions, counted by the Cayley number (n+ 1) n− 1, carry a natural
permutation representation of the symmetric group S n in which the number of orbits is the …

Rowmotion is a simple cyclic action on the distributive lattice of order ideals of a poset: it
sends the order ideal x to the order ideal generated by the minimal elements not in x. It can …

An n-core partition is an integer partition whose Young diagram contains no hook lengths
equal to n. We consider partitions that are simultaneously a-core and b-core for two …

We solve two open problems in Coxeter-Catalan combinatorics. First, we introduce a family
of rational noncrossing objects for any finite Coxeter group, using the combinatorics of …

For any finite path $ v $ on the square grid consisting of north and east unit steps, starting at
(0, 0), we construct a poset Tam $(v) $ that consists of all the paths weakly above $ v $ with …

In this paper, we exploit the combinatorics and geometry of triangulations of products of
simplices to derive new results in the context of Catalan combinatorics of $\nu $-Tamari …

The main objects of noncrossing Catalan combinatorics associated to a finite Coxeter
system are noncross-ing partitions, sortable elements, and cluster complexes. The first and …

We introduce the s-weak order on decreasing trees, a lattice which generalizes the classical
weak order on permutations. Restricting this lattice to certain trees gives rise to the s-Tamari …

The Catalan numbers constitute one of the most important sequences in combinatorics.
Catalan objects have been generalized in various directions, including the classical Fuss …