Abstract

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.

Disciplines

Mathematics

Number of Pages

33

Included in

Mathematics Commons

Share

COinS
 

URL: http://digitalcommons.calpoly.edu/math_fac/70