Related papers: Extending Fine sequences: a link with forbidden pa…

We construct generating trees with one, two, and three labels for some classes of permutations avoiding generalized patterns of length 3 and 4. These trees are built by adding at each level an entry to the right end of the permutation,…

Disjoint $n$-amalgamation is a condition on a complete first-order theory specifying that certain locally consistent families of types are also globally consistent. In this paper, we show that if a countably categorical theory $T$ admits an…

Vincular and covincular patterns are generalizations of classical patterns allowing restrictions on the indices and values of the occurrences in a permutation. In this paper we study the integer sequences arising as the enumerations of…

Despite the fact that the field of pattern avoiding permutations has been skyrocketing over the last two decades, there are very few exhaustive generating algorithms for such classes of permutations. In this paper we introduce the notions…

Starting from some considerations we make about the relations between certain difference statistics and the classical permutation statistics we study permutations whose inversion number and excedance difference coincide. It turns out that…

We investigate pattern avoidance in alternating permutations and generalizations thereof. First, we study pattern avoidance in an alternating analogue of Young diagrams. In particular, we extend Babson-West's notion of shape-Wilf…

In this paper we prove that among the permutations of length n with i fixed points and j excedances, the number of 321-avoiding ones equals the number of 132-avoiding ones, for all given i,j<=n. We use a new technique involving diagonals of…

In this note we count linear arrangements that avoid certain patterns and show their connection to the derangement numbers. We discuss the sequence Dn, which counts linear arrangements that avoid patterns 12, 23, ..., (n-1)n, n1, and show…

We study $321$-avoiding affine permutations, and prove a formula for their enumeration with respect to the inversion number by using a combinatorial approach. This is done in two different ways, both related to Viennot's theory of heaps.…

In this paper we investigate the geometry of a discrete Bayesian network whose graph is a tree all of whose variables are binary and the only observed variables are those labeling its leaves. We provide the full geometric description of…

We present four constructions of inversion sequences, and use them to compute the enumeration sequences of 24 classes of pattern-avoiding inversion sequences. This completes the enumeration of inversion sequences avoiding one or two…

Chen and collaborators give a recursively defined bijection from 021-avoiding ascent sequences to 021-avoiding (aka 132-avoiding) permutations. Here we give an algorithmic bijection from 021-avoiding ascent sequences to Dyck paths. Our…

In this paper, the problem of pattern avoidance in generalized non-crossing trees is studied. The generating functions for generalized non-crossing trees avoiding patterns of length one and two are obtained. Lagrange inversion formula is…

We establish a novel bijective encoding that represents permutations as forests of decorated (or enriched) trees. This allows us to prove local convergence of uniform random permutations from substitution-closed classes satisfying a…

We consider the problem of extending an acyclic binary relation that is invariant under a given family of transformations into an invariant preference. We show that when a family of transformations is commutative, every acyclic invariant…

The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…

We investigate various connections between the 0-Hecke monoid, Catalan monoid, and pattern avoidance in permutations, providing new tools for approaching pattern avoidance in an algebraic framework. In particular, we characterize…

We consider a large family of equivalence relations on permutations in Sn that generalise those discovered by Knuth in his study of the Robinson-Schensted correspondence. In our most general setting, two permutations are equivalent if one…

The pattern-avoiding fillings of Young diagrams we study arose from Postnikov's work on positive Grassman cells. They are called Le-diagrams, and are in bijection with decorated permutations. Other closely-related diagrams are interpreted…

We study an interesting family of cooperating coroutines, which is able to generate all patterns of bits that satisfy certain fairly general ordering constraints, changing only one bit at a time. (More precisely, the directed graph of…