Avgustinovich, Sergey and Kitaev, Sergey and Valyuzhenich, Alexander (2013) Avoidance of boxed mesh patterns on permutations. Discrete Applied Mathematics, 161 (1-2). pp. 43-51. ISSN 0166-218XFull text not available in this repository. Request a copy from the Strathclyde author
We introduce the notion of a boxed mesh pattern and study avoidance of these patterns on permutations. We prove that the celebrated former Stanley–Wilf conjecture is not true for all but eleven boxed mesh patterns; for seven out of the eleven patterns the former conjecture is true, while we do not know the answer for the remaining four (length-four) patterns. Moreover, we prove that an analogue of a well-known theorem of Erdős and Szekeres does not hold for boxed mesh patterns of lengths larger than 2. Finally, we discuss enumeration of permutations avoiding simultaneously two or more length-three boxed mesh patterns, where we meet generalized Catalan numbers.
|Keywords:||boxed mesh pattern, enumeration, Stanley–Wilf conjecture, Erdős–Szekeres theorem, generalized Catalan numbers, Electronic computers. Computer science, Discrete Mathematics and Combinatorics, Applied Mathematics|
|Subjects:||Science > Mathematics > Electronic computers. Computer science|
|Department:||Faculty of Science > Computer and Information Sciences|
|Depositing user:||Pure Administrator|
|Date Deposited:||17 Oct 2014 10:34|
|Last modified:||22 Mar 2017 13:35|