The Open University ’ s repository of research publications and other research outputs Permutations avoiding 1324 and patterns in
نویسنده
چکیده
The class Av(1324), of permutations avoiding the pattern 1324, is one of the simplest sets of combinatorial objects to define that has, thus far, failed to reveal its enumerative secrets. By considering certain large subsets of the class, which consist of permutations with a particularly regular structure, we prove that the growth rate of the class exceeds 9.81. This improves on a previous lower bound of 9.47. Central to our proof is an examination of the asymptotic distributions of certain substructures in the Hasse graphs of the permutations. In this context, we consider occurrences of patterns in Lukasiewicz paths and prove that in the limit they exhibit a concentrated Gaussian distribution.
منابع مشابه
The Open University ’ s repository of research publications and other research outputs Permutations avoiding 1324 and patterns in Lukasiewicz paths
The class Av(1324), of permutations avoiding the pattern 1324, is one of the simplest sets of combinatorial objects to define that has, thus far, failed to reveal its enumerative secrets. By considering certain large subsets of the class, which consist of permutations with a particularly regular structure, we prove that the growth rate of the class exceeds 9.81. This improves on a previous lowe...
متن کاملresearch publications and other research outputs Permutations avoiding 1324 and patterns in
The class Av(1324), of permutations avoiding the pattern 1324, is one of the simplest sets of combinatorial objects to define that has, thus far, failed to reveal its enumerative secrets. By considering certain large subsets of the class, which consist of permutations with a particularly regular structure, we prove that the growth rate of the class exceeds 9.81. This improves on a previous lowe...
متن کامل’ s repository of research publications and other research outputs The enumeration of permutations avoiding 2143 and 4231
We enumerate the pattern class Av(2143, 4231) and completely describe its permutations. The main tools are simple permutations and monotone grid classes.
متن کاملThe Open University ’ s repository of research publications and other research outputs 2 monotone grid classes are finitely based
The Open University's repository of research publications and other research outputs 2 monotone grid classes are finitely based Journal Article Copyright and Moral Rights for the articles on this site are retained by the individual authors and/or other copyright owners. For more information on Open Research Online's data policy on reuse of materials please consult the policies page. In this not...
متن کاملThe Open University ’ s repository of research publications and other research outputs 2 monotone grid classes are finitely
The Open University's repository of research publications and other research outputs 2 monotone grid classes are finitely based Journal Article Copyright and Moral Rights for the articles on this site are retained by the individual authors and/or other copyright owners. For more information on Open Research Online's data policy on reuse of materials please consult the policies page. In this not...
متن کامل