Related papers: Permutations Which Avoid 1243 and 2143, Continued …

Several authors have examined connections among restricted permutations, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues of these results for involutions which avoid 3412. Our results…

We study generating functions for the number of involutions in $S_n$ avoiding (or containing once) 132, and avoiding (or containing once) an arbitrary permutation $\tau$ on $k$ letters. In several interesting cases the generating function…

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…

A permutation is said to be \emph{alternating} if it starts with rise and then descents and rises come in turn. In this paper we study the generating function for the number of alternating permutations on $n$ letters that avoid or contain…

We determine the structure of permutations avoiding the patterns 4213 and 2143. Each such permutation consists of the skew sum of a sequence of plane trees, together with an increasing sequence of points above and an increasing sequence of…

We show that the counting sequence for permutations avoiding both of the (classical) patterns 1243 and 2134 has the algebraic generating function supplied by Vaclav Kotesovec for sequence A164651 in The On-Line Encyclopedia of Integer…

Let f_n^r(k) be the number of 132-avoiding permutations on n letters that contain exactly r occurrences of 12... k, and let F_r(x;k) and F(x,y;k) be the generating functions defined by $F_r(x;k)=\sum_{n\gs0} f_n^r(k)x^n$ and…

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

Egge and Mansour have recently studied permutations which avoid 1243 and 2143 regarding the occurrence of certain additional patterns. Some of the open questions related to their work can easily be answered by using permutation diagrams.…

We study generating functions for the number of involutions, even involutions, and odd involutions in $S_n$ subject to two restrictions. One restriction is that the involution avoid 3412 or contain 3412 exactly once. The other restriction…

We extend earlier work of the same author to enumerate alternating permutations avoiding the permutation pattern 2143. We use a generating tree approach to construct a recursive bijection between the set A_{2n}(2143) of alternating…

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.

We study generating functions for the number of permutations on n letters avoiding 132 and an arbitrary permutation $\tau$ on k letters, or containing $\tau$ exactly once. In several interesting cases the generating function depends only on…

We study generating functions for the number of even (odd) permutations on n letters avoiding 132 and an arbitrary permutation $\tau$ on k letters, or containing $\tau$ exactly once. In several interesting cases the generating function…

This short paper is concerned with the enumeration of permutations avoiding the following four patterns: $2431$, $4231$, $1432$ and $4132$. Using a bijective construction, we prove that these permutations are counted by the central binomial…

We enumerate the pattern class Av(2143,4231) and completely describe its permutations. The main tools are simple permutations and monotone grid classes.

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 study generating functions for the number of permutations in $S_n$ subject to set of restrictions. One of the restrictions belongs to $S_3$, while the others to $S_k$. It turns out that in a large variety of cases the answer can be…

We study the longest increasing subsequence problem for random permutations avoiding the pattern $312$ and another pattern $\tau$ under the uniform probability distribution. We determine the exact and asymptotic formulas for the average…

We use catalytic variables to derive generating functions for the permutation classes $Av(\textbf{4123},\textbf{1324})$, $Av(\textbf{4123},\textbf{1243})$, and $Av(\textbf{4123},\textbf{1342})$. Each generating function is algebraic of…