Alternating permutations and binary increasing trees
نویسندگان
چکیده
منابع مشابه
Increasing trees and alternating permutations
In this article we consider some increasing trees, the number of which is equal to the number of alternating (updown) permutations, that is, permutations of the form σ(1) < σ(2) > σ(3) < ... . It turns out that there are several such classes of increasing trees, each of which is interesting in itself. Special attention is paid to the study of various statistics on these trees, connected with th...
متن کاملGenerating Trees and Pattern Avoidance in Alternating Permutations
We extend earlier work of the same author to enumerate alternating permutations avoiding the permutation pattern 2143. We use a generating tree approach to construct a recursive bijection between the set A2n(2143) of alternating permutations of length 2n avoiding 2143 and the set of standard Young tableaux of shape 〈n, n, n〉, and between the set A2n+1(2143) of alternating permutations of length...
متن کاملGeneralized Stirling permutations, families of increasing trees and urn models
Bona [6] studied the distribution of ascents, plateaux and descents in the class of Stirling permutations, introduced by Gessel and Stanley [14]. Recently, Janson [18] showed the connection between Stirling permutations and plane recursive trees and proved a joint normal law for the parameters considered by Bona. Here we will consider generalized Stirling permutations extending the earlier resu...
متن کاملAlternating, Pattern-Avoiding Permutations
We study the problem of counting alternating permutations avoiding collections of permutation patterns including 132. We construct a bijection between the set Sn(132) of 132-avoiding permutations and the set A2n+1(132) of alternating, 132avoiding permutations. For every set p1, . . . , pk of patterns and certain related patterns q1, . . . , qk, our bijection restricts to a bijection between Sn(...
متن کاملParity-alternating permutations and successions
The study of parity-alternating permutations of {1, 2, . . . , n} is extended to permutations containing a prescribed number of parity successions – adjacent pairs of elements of the same parity. Several enumeration formulae are computed for permutations containing a given number of parity successions, in conjunction with further parity and length restrictions. The objects are classified using ...
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: 1975
ISSN: 0097-3165
DOI: 10.1016/0097-3165(75)90002-3