On avoidance of V- and ^-patterns in permutations
نویسندگان
چکیده
We study Vand Λ-patterns which generalize valleys and peaks, as well as increasing and decreasing runs, in permutations. A complete classification of permutations (multi)-avoiding Vand Λ-patterns of length 4 is given. We also establish a connection between restricted permutations and matchings in the coronas of complete graphs.
منابع مشابه
New Equivalences for Pattern Avoidance for Involutions
We complete the Wilf classification of signed patterns of length 5 for both signed permutations and signed involutions. New general equivalences of patterns are given which prove Jaggard’s conjectures concerning involutions in the symmetric group avoiding certain patterns of length 5 and 6. In this way, we also complete the Wilf classification of S5, S6, and S7 for both permutations and involut...
متن کاملPattern Avoidance in Labelled Trees
We discuss a new notion of pattern avoidance motivatedby operad theory: pattern avoidance in planar labelled trees. It is a generalisation of various types of consecutive pattern avoidance studied before: consecutive patterns in words, permutations, colouredpermutations, etc. ThenotionofWilf equivalence for patterns in permutations admits a straightforward generalisation for (sets of) tree patt...
متن کاملMultiple Pattern Avoidance with respect to Fixed Points and Excedances
We study the distribution of the statistics ‘number of fixed points’ and ‘number of excedances’ in permutations avoiding subsets of patterns of length 3. We solve all the cases of simultaneous avoidance of more than one pattern, giving generating functions enumerating these two statistics. Some cases are generalized to patterns of arbitrary length. For avoidance of one single pattern we give pa...
متن کاملPattern Avoidance in Partial Permutations
Motivated by the concept of partial words, we introduce an analogous concept of partial permutations. A partial permutation of length n with k holes is a sequence of symbols π = π1π2 · · · πn in which each of the symbols from the set {1, 2, . . . , n− k} appears exactly once, while the remaining k symbols of π are “holes”. A. Claesson, V. Jeĺınek and S. Kitaev were supported by the Icelandic Re...
متن کاملOn the sub-permutations of pattern avoiding permutations
There is a deep connection between permutations and trees. Certain sub-structures of permutations, called sub-permutations, bijectively map to sub-trees of binary increasing trees. This opens a powerful tool set to study enumerative and probabilistic properties of sub-permutations and to investigate the relationships between ’local’ and ’global’ features using the concept of pattern avoidance. ...
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:
- Ars Comb.
دوره 97 شماره
صفحات -
تاریخ انتشار 2010