Avoidance of boxed mesh patterns on permutations

Sergey Avgustinovich, Sergey Kitaev, Alexandr Valyuzhenich
2013 Discrete Applied Mathematics  
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
more » ... than 2. Finally, we discuss enumeration of permutations avoiding simultaneously two or more length-three boxed mesh patterns, where we meet generalized Catalan numbers.
doi:10.1016/j.dam.2012.08.015 fatcat:gsdyihucfzetnky4trw647nkfm