相关论文: Restricted 3412-Avoiding Involutions: Continued Fr…
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…
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…
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…
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…
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…
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 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…
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 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…
We show that permutations avoiding both of the (classical) patterns 4321 and 3241 have the algebraic generating function conjectured by Vladimir Kruchinin.
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 $\SS_n$ subject to two restrictions. One of the restrictions belongs to $\SS_3$, while the other to $\SS_k$. It turns out that in a large variety of cases the answer can be…
We find, in the form of a continued fraction, the generating function for the number of (132)-avoiding permutations that have a given number of (123) patterns, and show how to extend this to permutations that have exactly one (132) pattern.…
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 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…
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 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…
In [GM] Guibert and Mansour studied involutions on n letters avoiding (or containing exactly once) 132 and avoiding (or containing exactly once) an arbitrary pattern on k letters. They also established a bijection between 132-avoiding…
We consider the problem of enumerating permutations with exactly r occurrences of the pattern 1324 and derive functional equations for this general case as well as for the pattern avoidance (r=0) case. The functional equations lead to a new…
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…