Related papers: On the diagram of 132-avoiding permutations
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.…
The theme of this article is a "reciprocity" between bounded up-down paths and bounded alternating sequences. Roughly speaking, this ``reciprocity" manifests itself by the fact that the extension of the sequence of numbers of paths of…
We initiate a systematic study of pattern avoidance in rectangulations. We give a formal definition of such patterns and investigate rectangulations that avoid $\top$-like patterns - the pattern $\top$ and its rotations. For every $L…
A permutation $\pi$ contains a pattern $\sigma$ if and only if there is a subsequence in $\pi$ with its letters are in the same relative order as those in $\sigma$. Partially ordered patterns (POPs) provide a convenient way to denote…
We present combinatorial bijections and identities between certain skew Young tableaux, Dyck paths, triangulations, and dissections.
The study of pattern avoidance in permutations, and specifically in flattened partitions is an active area of current research. In this paper, we count the number of distinct flattened partitions over [n] avoiding a single pattern, as well…
A bijection is defined from Littlewood-Richardson tableaux to rigged configurations. It is shown that this map preserves the appropriate statistics, thereby proving a quasi-particle expression for the generalized Kostka polynomials, which…
In this paper we consider the enumeration of ordered set partitions avoiding a permutation pattern of length 2 or 3. We provide an exact enumeration for avoiding the permutation 12. We also give exact enumeration for ordered partitions with…
Motivated by the concept of partial words, we introduce an analogous concept of partial permutations. A partial permutation of length n with k holes is a sequence of symbols $\pi = \pi_1\pi_2 ... \pi_n$ in which each of the symbols from the…
We present a new bijection between variants of $m$-Dyck paths (paths with steps in $\{+1,-m\}$ starting and ending at height $0$ and remaining at non-negative height), which generalizes a classical bijection between Dyck prefixes and…
The class Av(1324), of permutations avoiding the pattern 1324, is one of the simplest sets of combinatorial objects to define that has, thus far, failed to reveal its enumerative secrets. By considering certain large subsets of the class,…
We consider avoidance of permutation patterns with designated gap sizes between pairs of consecutive letters. We call the patterns having such constraints distant patterns (DPs) and we show their relation to other pattern notions…
The research on pattern-avoidance has yielded so far limited knowledge on Wilf-ordering of permutations. The Stanley-Wilf limits sqrt[n](|S_n(tau)|) and further works suggest asymptotic ordering of layered versus monotone patterns. Yet,…
We study a subset of permutations, where entries are restricted to having the same remainder as the index, modulo some integer $k \geq 2$. We show that when also imposing the classical 132- or 213-avoidance restriction on the permutations,…
This addendum contains results about the inversion number and major index polynomials for permutations avoiding 321 which did not fit well into the original paper. In particular, we consider symmetry, unimodality, behavior modulo 2, and…
Pattern avoidance in the symmetric group $S_n$ has provided a number of useful connections between seemingly unrelated problems from stack-sorting to Schubert varieties. Recent work has generalized these results to $S_n\wr C_c$, the objects…
We study shifted standard Young tableaux (SYT). The limiting surface of uniformly random shifted SYT of staircase shape is determined, with the integers in the SYT as heights. This implies via properties of the Edelman-Greene bijection…
We initiate an in-depth study of pattern avoidance on modified ascent sequences. Our main technique consists in using Stanley's standardization to obtain a transport theorem between primitive modified ascent sequences and permutations…
We present a simplified variant of Biane's bijection between permutations and 3-colored Motzkin paths with weight that keeps track of the inversion number, excedance number and a statistic so-called depth of a permutation. This generalizes…