A New Upper Bound for 1324-Avoiding Permutations
نویسنده
چکیده
We prove that the number of 1324-avoiding permutations of length n is less than (7 + 4 √ 3). The novelty of our method is that we injectively encode such permutations by a pair of words of length n over a finite alphabet that avoid a given factor.
منابع مشابه
A structural characterisation of Av(1324) and new bounds on its growth rate
We establish an improved lower bound of 10.271 for the exponential growth rate of the class of permutations avoiding the pattern 1324, and an improved upper bound of 13.5. These results depend on a new exact structural characterisation of 1324-avoiders as a subclass of an infinite staircase grid class, together with precise asymptotics of a small domino subclass whose enumeration we relate to W...
متن کاملNew bounds on the growth rate of 1324-avoiders
We establish an improved lower bound of 10.271 for the exponential growth rate of the class of permutations avoiding the pattern 1324, and an improved upper bound of 13.5. These results depend on a new exact structural characterisation of 1324-avoiders as a subclass of an infinite staircase grid class, together with precise asymptotics of a small “domino” subclass whose enumeration is related t...
متن کاملThe 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 کاملThe Open University ’ s repository of research 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...
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ورودعنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 23 شماره
صفحات -
تاریخ انتشار 2014