Kitaev, Sergey and Mansour, Toufik (2005) On multi-avoidance of generalized patterns. Ars Combinatoria, 76. pp. 321-350.Full text not available in this repository. (Request a copy from the Strathclyde author)
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 n-permutations are 2n−1, the number of involutions in n, and 2En, where En is the n-th Euler number. In this paper we give recurrence relations for the remaining three essentially different cases. To complete the descriptions in [Kit3] and [KitMans], we consider avoidance of a pattern of the form x−y−z (a classical 3-pattern) and beginning or ending with an increasing or decreasing pattern. Moreover, we generalize this problem: we demand that a permutation must avoid a 3-pattern, begin with a certain pattern and end with a certain pattern simultaneously. We find the number of such permutations in case of avoiding an arbitrary generalized 3-pattern and beginning and ending with increasing or decreasing patterns.
|Keywords:||generalized patterns, increasing pattern, decreasing pattern, Electronic computers. Computer science, Mathematics(all)|
|Subjects:||Science > Mathematics > Electronic computers. Computer science|
|Department:||Faculty of Science > Computer and Information Sciences|
|Depositing user:||Pure Administrator|
|Date Deposited:||14 Oct 2014 13:59|
|Last modified:||07 Jan 2017 04:17|