Related papers: Some statistics on restricted 132 involutions
An infinte word w avoids a pattern p with the involution t if there is no substitution for the variables in p and no involution t such that the resulting word is a factor of w. We investigate the avoidance of patterns with respect to the…
We study the generating function for the number of permutations on n letters containing exactly $r\gs0$ occurences of 132. It is shown that finding this function for a given r amounts to a routine check of all permutations in $S_{2r}$.
We present a method, illustrated by several examples, to find explicit counts of permutations containing a given multiset of three letter patterns. The method is recursive, depending on bijections to reduce to the case of a smaller…
In this paper we study the enumeration and the construction, according to the number of ones, of particular binary words avoiding a fixed pattern. The growth of such words can be described by particular jumping and marked succession rules.…
We study the total number of occurrences of several vincular (also called generalized) patterns and other statistics, such as the major index and the Denert statistic, on permutations avoiding a pattern of length 3, extending results of…
It is well-known, and was first established by Knuth in 1969, that the number of 321-avoiding permutations is equal to that of 132-avoiding permutations. In the literature one can find many subsequent bijective proofs of this fact. It turns…
A bijection between $(31245,32145,31254,32154)$-avoiding permutations and $(31425,32415,31524,32514)$-avoiding permutations is constructed, which preserves five classical set-valued statistics. Combining with two codings of permutations due…
We define a class L_{n, k} of permutations that generalizes alternating (up-down) permutations and give bijective proofs of certain pattern-avoidance results for this class. As a special case of our results, we give two bijections between…
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…
We complete the enumeration of Dumont permutations of the second kind avoiding a pattern of length 4 which is itself a Dumont permutation of the second kind. We also consider some combinatorial statistics on Dumont permutations avoiding…
Recently, a new class of words, denoted by L_n, was shown to be in bijection with a subset of the Dyck paths of length 2n having cardinality given by the (n-1)-st Catalan number. Here, we consider statistics on L_n recording the number of…
Several authors have examined connections between permutations which avoid 132, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues of some of these results for permutations which avoid 1243…
In this paper, we compute the distribution of the first letter statistic on nine avoidance classes of permutations corresponding to two pairs of patterns of length four. In particular, we show that the distribution is the same for each…
We study the joint distribution of descents and inverse descents over the set of permutations of n letters. Gessel conjectured that the two-variable generating function of this distribution can be expanded in a given basis with nonnegative…
Catalan words are particular growth-restricted words over the set of non-negative integers, and they represent still another combinatorial class counted by the Catalan numbers. We study the distribution of descents on the sets of Catalan…
We study the descent distribution over the set of centrosymmetric permutations that avoid the pattern of length 3. Our main tool in the most puzzling case, namely, $\tau=123$ and $n$ even, is a bijection that associates a Dyck prefix of…
Two $k$-ary Fibonacci recurrences are $a_k(n) = a_k(n-1) + k \cdot a_k(n-2)$ and $b_k(n) = k \cdot b_k(n-1) + b_k(n-2)$. We provide a simple proof that $a_k(n)$ is the number of $k$-regular words over $[n] = \{1,2,\ldots,n\}$ that avoid…
Not long ago, Claesson and Mansour proposed some conjectures about the enumeration of the permutations avoiding more than three Babson - Steingr\'\i msson patterns (generalized patterns of type $(1,2)$ or $(2,1)$). The avoidance of one, two…
Enumeration problems related to words avoiding patterns as well as permutations that contain the pattern $123$ exactly once have been studied in great detail. However, the problem of enumerating words that contain the pattern $123$ exactly…
In this paper, we compute and demonstrate the equivalence of the joint distribution of the first letter and descent statistics on six avoidance classes of permutations corresponding to two patterns of length four. This distribution is in…