Cyclic and lift closures for k...21-avoiding permutations
نویسنده
چکیده
We prove that the cyclic closure of the permutation class avoiding the pattern k(k− 1) . . . 21 is finitely based. The minimal length of a minimal permutation is 2k − 1 and these basis permutations are enumerated by (2k− 1).ck where ck is the kth Catalan number. We also define lift operations and give similar results. Finally, we consider the toric closure of a class and we propose some open problems.
منابع مشابه
On a Refinement of Wilf-equivalence for Permutations
Recently, Dokos et al. conjectured that for all k,m > 1, the patterns 12 . . . k(k+ m+ 1) . . . (k + 2)(k + 1) and (m+ 1)(m+ 2) . . . (k +m+ 1)m. . . 21 are maj-Wilfequivalent. In this paper, we confirm this conjecture for all k > 1 and m = 1. In fact, we construct a descent set preserving bijection between 12 . . . k(k−1)-avoiding permutations and 23 . . . k1-avoiding permutations for all k > ...
متن کاملCyclically closed pattern classes of permutations
The cyclic closure of a permutation pattern class is defined as the set of all the cyclic rotations of its permutations. Examples of finitely based classes whose cyclic closure is also finitely based are given, as well as an example where the cyclic closure is not finitely based. Some enumerations of cyclic closures are computed.
متن کاملAVOIDANCE OF PARTIALLY ORDERED PATTERNS OF THE FORM k-σ-k
Sergey Kitaev [4] has shown that the exponential generating function for permutations avoiding the generalized pattern σ-k, where σ is a pattern without dashes and k is one greater than the largest element in σ, is determined by the exponential generating function for permutations avoiding σ. We show that the exponential generating function for permutations avoiding the partially ordered patter...
متن کاملGenerating-tree isomorphisms for pattern-avoiding involutions∗
We show that for k ≥ 5 and the permutations τk = (k − 1)k(k − 2) . . . 312 and Jk = k(k − 1) . . . 21, the generating tree for involutions avoiding the pattern τk is isomorphic to the generating tree for involutions avoiding the pattern Jk. This implies a family of Wilf equivalences for pattern avoidance by involutions; at least the first member of this family cannot follow from any type of pre...
متن کاملPattern Avoidance in Permutations: Linear and Cyclic Orders
We generalize the notion of pattern avoidance to arbitrary functions on ordered sets, and consider specifically three scenarios for permutations: linear, cyclic and hybrid, the first one corresponding to classical permutation avoidance. The cyclic modification allows for circular shifts in the entries. Using two bijections, both ascribable to both Deutsch and Krattenthaler independently, we sin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Mathematics
دوره 311 شماره
صفحات -
تاریخ انتشار 2011