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Consecutive patterns: from permutations to column-convex polyominoes and back
The electronic journal of combinatorics, Tome 17 (2010)
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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.
DOI : 10.37236/334
Classification : 05A15 
@article{10_37236_334,
     author = {Don Rawlings and Mark Tiefenbruck},
     title = {Consecutive patterns: from permutations to column-convex polyominoes and back},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/334},
     zbl = {1189.05015},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/334/}
}
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%A Don Rawlings
%A Mark Tiefenbruck
%T Consecutive patterns: from permutations to column-convex polyominoes and back
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Don Rawlings; Mark Tiefenbruck. Consecutive patterns: from permutations to column-convex polyominoes and back. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/334

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