Published in Electronic Journal of Combinatorics, Volume 17, Issue 1, April 19, 2010.
Copyright © 2010 Don Rawlings and Mark Tiefenbruck. Published by Electronic Journal of Combinatorics.
We expose the ties between the consecutive pattern enumeration problems associated with permutations, compositions, column-convex polyominoes, and words. Our perspective allows powerful methods from the contexts of compositions, column-convex polyominoes, and of words to be applied directly to the enumeration of permutations by consecutive patterns. We deduce a host of new consecutive pattern results,including a solution to the (2m+1)-alternating pattern problem on permutations posed by Kitaev.