منابع مشابه
Restricted 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 Dumont permutations
We analyze the structure and enumerate Dumont permutations of the first and second kinds avoiding certain patterns or sets of patterns of length 3 and 4. Some cardinalities are given by Catalan numbers, powers of 2, little Schröder numbers, and other known or related sequences.
متن کاملRestricted Dumont permutations, Dyck paths, and noncrossing partitions
We complete the enumeration of Dumont permutations of the second kind avoiding a pattern of length 4 which is itself a Dumont permutation of the second kind. We also consider some combinatorial statistics on Dumont permutations avoiding certain patterns of length 3 and 4 and give a natural bijection between 3142-avoiding Dumont permutations of the second kind and noncrossing partitions that use...
متن کاملDumont permutations of the third kind
We consider the set of permutations all of whose descents are from an even value to an even value. Proving a conjecture of Kitaev and Remmel, we show that these permutations are enumerated by Genocchi numbers, hence equinumerous to Dumont permutations of the first (and second) kind, and thus may be called Dumont permutations of the third kind. We also define the related Dumont permutations of t...
متن کاملRestricted permutations
Restricted permutations are those constrained by having to avoid subsequences ordered in various prescribed ways. They have functioned as a convenient descriptor for several sets of permutations which arise naturally in combinatorics and computer science. We study the partial order on permutations (and more general sequences) that underlies the idea of restriction and which gives rise to sets o...
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2005
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-005-0256-4