Permutations with one or two 132-subsequences
نویسندگان
چکیده
منابع مشابه
Permutations with one or two 132-subsequences
We prove a strikingly simple formula for the number of permutations containing exactly one subsequence of type 132. We show that this number equals the number of partitions of a convex (n + 1 )-gon into n 2 parts by noncrossing diagonals. We also prove a recursive formula for the number d, of those containing exactly two such subsequences, yielding that {d,} is P-recursive. (~) 1998 Elsevier Sc...
متن کاملPermutations with short monotone subsequences
We consider permutations of 1, 2, ..., n whose longest monotone subsequence is of length n and are therefore extremal for the Erdős-Szekeres theorem. Such permutations correspond via the Robinson-Schensted correspondence to pairs of square n × n Young tableaux. We show that all the bumping sequences are constant and therefore these permutations have a simple description in terms of the pair of ...
متن کاملLongest subsequences in permutations
For a class of permutations X the LXS problem is to identify in a given permutation σ of length n its longest subsequence that is isomorphic to a permutation of X . In general LXS is NP-hard. A general construction that produces polynomial time algorithms for many classes X is given. More efficient algorithms are given when X is defined by avoiding some set of permutations of length 3.
متن کاملRestricted 132-Dumont permutations
A permutation π is said to be a Dumont permutation of the first kind if each even integer in π must be followed by a smaller integer, and each odd integer is either followed by a larger integer or is the last element of π (see, for example, www.theory.csc.uvic.ca/∼cos/inf/perm/Genocchi Info.html). In Duke Math. J. 41 (1974), 305–318, Dumont showed that certain classes of permutations on n lette...
متن کاملRestricted 132-avoiding permutations
We study generating functions for the number of permutations on n letters avoiding 132 and an arbitrary permutation τ on k letters, or containing τ exactly once. In several interesting cases the generating function depends only on k and is expressed via Chebyshev polynomials of the second kind. 2000 Mathematics Subject Classification: Primary 05A05, 05A15; Secondary 30B70, 42C05
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: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(97)00062-9