Simple permutations and algebraic generating functions
نویسندگان
چکیده
منابع مشابه
Simple permutations and algebraic generating functions
A simple permutation is one that does not map a nontrivial interval onto an interval. It was recently proved by Albert and Atkinson that a permutation class with only finitely simple permutations has an algebraic generating function. We extend this result to enumerate permutations in such a class satisfying additional properties, e.g., the even permutations, the involutions, the permutations av...
متن کاملGenerating and Enumerating 321-Avoiding and Skew-Merged Simple Permutations
The simple permutations in two permutation classes — the 321-avoiding permutations and the skew-merged permutations — are enumerated using a uniform method. In both cases, these enumerations were known implicitly, by working backwards from the enumeration of the class, but the simple permutations had not been enumerated explicitly. In particular, the enumeration of the simple skew-merged permut...
متن کاملConsecutive patterns in permutations: clusters and generating functions
We use the cluster method in order to enumerate permutations avoiding consecutive patterns. We reprove and generalize in a unified way several known results and obtain new ones, including some patterns of length 4 and 5, as well as some infinite families of patterns of a given shape. Our main tool is the cluster method of Goulden and Jackson. We also prove some that, for a large class of patter...
متن کاملClusters, generating functions and asymptotics for consecutive patterns in permutations
Article history: Received 27 January 2012 Accepted 9 August 2012 Available online 5 September 2012 MSC: primary 05A05 secondary 05A15, 06A07
متن کاملGenerating Permutations and Combinations
We consider permutations of {1, 2, . . . , n} in which each integer is given a direction; such permutations are called directed permutations. An integer k in a directed permutation is called mobile of its arrow points to a smaller integer adjacent to it. For example, for → 3 → 2 ← 5 → 4 → 6 → 1 , the integers 3, 5, and 6 are mobile. It follows that 1 can never be mobile since there is no intege...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2008
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2007.06.007