Related papers: Restricted 3412-Avoiding Involutions: Continued Fr…

A permutation is called Grassmannian if it has at most one descent. In this paper, we investigate pattern avoidance and parity restrictions for such permutations. As our main result, we derive formulas for the enumeration of Grassmannian…

In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…

Inspired by the definition of modified ascent sequences, we introduce a new class of integer sequences called revised ascent sequences. These sequences are defined as Cayley permutations where each entry is a leftmost occurrence if and only…

A simple permutation is one that does not map a nontrivial interval onto an interval. It was recently proved by Albert and Atkinson that a permutation class with only finitely simple permutations has an algebraic generating function. We…

Recently, degenerate Cauchy numbers and polynomials are introduced in [10]. In this paper, we study the degenerate Cauchy numbers and polynomials which are different from the previous degenerate Cauchy numbers and polynomials. In addition,…

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 show that very simple continued fractions can be obtained for the ordinary generating functions enumerating permutations or D-permutations with a large number of independent statistics, when each cycle is given a weight $-1$. The proof…

Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one's attention to indecomposable permutations. In the style of the seminal paper by Simion…

This paper considers functional series whose terms are higher-order derivatives of Chebyshev polynomials of the second kind, where the degree of the polynomial is related to the order of the derivative. Analytic summation is used to…

In [Kit1] Kitaev discussed simultaneous avoidance of two 3-patterns with no internal dashes, that is, where the patterns correspond to contiguous subwords in a permutation. In three essentially different cases, the numbers of such…

In [BS] Babson and Steingrimsson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Let $f_{\tau;r}(n)$ be the number of $1\mn3\mn2$-avoiding…

We provide a simple injective proof that the number of 132-avoiding permutations with a unique longest increasing subsequence is at least as large as the number of 132-avoiding permutations without a unique longest increasing subsequence.

Three complementation-like involutions are constructed on permutations to prove, and in some cases generalize, all remaining fourteen joint symmetric equidistribution conjectures of Lv and Zhang. Further enumerative results are obtained for…

We present bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (2+2)-free posets and a certain class of involutions (or chord diagrams), already appeared in the literature, but were apparently not…

We construct a bijection between $321$- and $213$-avoiding permutations that preserves the property of $t$-stack-sortability. Our bijection transforms natural statistics between these two classes of permutations and proves a refinement of…

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…

We study aspects of the enumeration of permutation classes, sets of permutations closed downwards under the subpermutation order. First, we consider monotone grid classes of permutations. We present procedures for calculating the generating…

We enumerate and characterize some classes of alternating and reverse alternating involutions avoiding a single pattern of length three or four. If on one hand the case of patterns of length three is trivial, on the other hand, the length…

Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…

We give some results about a bijection associating each permutation with a subexcedant function. This function is related to a particular decomposition of the permutation as a product of transpositions and therefore it has been called…