Related papers: The fine structure of 321 avoiding involutions

We study the fine structure of the sets of involutions avoiding either 4312 (I(4321)) or 3412 (I(3412)), connecting the point of view of the decomposition theorems with the one of the associated labelled Motzkin paths. The algebraic…

We use combinatorial and generating function techniques to enumerate various sets of involutions which avoid 231 or contain 231 exactly once. Interestingly, many of these enumerations can be given in terms of $k$-generalized Fibonacci…

Bivariate generating functions for various subsets of the class of permutations containing no descending sequence of length three or more are determined. The notion of absolute indecomposability of a permutation is introduced, and used in…

We show how a bijection due to Biane between involutions and labelled Motzkin paths yields bijections between Motzkin paths and two families of restricted involutions that are counted by Motzkin numbers, namely, involutions avoiding 4321…

We show that permutations avoiding both of the (classical) patterns 4321 and 3241 have the algebraic generating function conjectured by Vladimir Kruchinin.

A 321-k-gon-avoiding permutation pi avoids 321 and the following four patterns: k(k+2)(k+3)...(2k-1)1(2k)23...(k+1), k(k+2)(k+3)...(2k-1)(2k)123...(k+1), (k+1)(k+2)(k+3)...(2k-1)1(2k)23...k, (k+1)(k+2)(k+3)...(2k-1)(2k)123...k. The…

We exhibit a bijection between 132-avoiding permutations and Dyck paths. Using this bijection, it is shown that all the recently discovered results on generating functions for 132-avoiding permutations with a given number of occurrences of…

We find the generating function for the class of all permutations that avoid the patterns 3124 and 4312 by showing that it is an inflation of the union of two geometric grid classes.

The 321,hexagon-avoiding (321-hex) permutations were introduced and studied by Billey and Warrington in as a class of elements of S_n whose Kazhdan-Lusztig and Poincare polynomials and the singular loci of whose Schubert varieties have…

In this paper, we characterize and enumerate pattern-avoiding permutations composed of only 3-cycles. In particular, we answer the question for the six patterns of length 3. We find that the number of permutations composed of $n$ 3-cycles…

We enumerate several classes of pattern-avoiding rectangulations. We establish new bijective links with pattern-avoiding permutations, prove that their generating functions are algebraic, and confirm several conjectures by Merino and…

The simple permutations in two permutation classes --- the 321-avoiding permutations and the skew-merged permutations --- are enumerated using a uniform method. In both cases, these enumerations were known implicitly, by working backwards…

We show that cyclic permutations avoiding $321$ are precisely those permutations whose image under the fundamental bijection avoid a set of vincular patterns. We do this by using pattern functions and arrow patterns, in combination with the…

Let $A_k$ be the set of permutations in the symmetric group $S_k$ with prefix 12. This paper concerns the enumeration of involutions which avoid the set of patterns $A_k$. We present a bijection between symmetric Schroder paths of length…

Using a recursive approach, we show that the generating function for sets of Motzkin paths avoiding a single (not necessarily consecutive) pattern is rational over $x$ and the Catalan generating function $C(x) =…

We give an improved algorithm for counting the number of $1324$-avoiding permutations, resulting in 5 further terms of the generating function. We analyse the known coefficients and find compelling evidence that unlike other classical…

This paper completes a project to enumerate permutations avoiding a triple T of 4-letter patterns, in the sense of classical pattern avoidance, for every T. There are 317 symmetry classes of such triples T and previous papers have…

We derive the algebraic generating function for inversion sequences avoiding the patterns $201$ and $210$ by describing a set of succession rules, converting them to a system of generating function equations with one catalytic variable, and…

The maximally clustered permutations are characterized by avoiding the classical permutation patterns 3421, 4312, and 4321. This class contains the freely-braided permutations and the fully-commutative permutations. In this work, we show…

For a variety of pattern-avoiding classes, we describe the limiting distribution for the number of fixed points for involutions chosen uniformly at random from that class. In particular we consider monotone patterns of arbitrary length as…