Runs in labelled trees and mappings
نویسندگان
چکیده
منابع مشابه
Pattern Avoidance in Labelled Trees
We discuss a new notion of pattern avoidance motivatedby operad theory: pattern avoidance in planar labelled trees. It is a generalisation of various types of consecutive pattern avoidance studied before: consecutive patterns in words, permutations, colouredpermutations, etc. ThenotionofWilf equivalence for patterns in permutations admits a straightforward generalisation for (sets of) tree patt...
متن کاملMonotonically labelled Motzkin trees
Consider a rooted tree structure the nodes of which have been labelled monotonically by elements of { 1, 2, . . .,k}, which means that any sequence connecting the root of the tree with a leaf is weakly monotone . For fixed k asymptotic equivalents of the form CA gA °n; 2 (n --oo) to the numbers of such tree structures with n nodes are obtained for the family of extended unary-binary trees (i .e...
متن کاملEnumeration of Some Labelled Trees
In this paper we are interesting in the enumeration of rooted labelled trees according to the relationship between the root and its sons. Let Tn;k be the family of Cayley trees on n] such that the root has exactly k smaller sons. In a rst time we give a bijective proof of the fact that jTn+1;kj = ? n k n n?k. Moreover, we use the family Tn+1;0 of Cayley trees for which the root is smaller than ...
متن کاملEmbeddings and Other Mappings of Rooted Trees Into Complete Trees
Let Tn be the complete binary tree of height n, with root 1n as the maximum element. For T a tree, define A(n;T ) = |{S ⊆ Tn : 1n ∈ S, S ∼= T}| and C(n;T ) = |{S ⊆ Tn : S ∼= T}|. We disprove a conjecture of Kubicki, Lehel and Morayne, which claims that A(n;T1) C(n;T1) ≤ A(n;T2) C(n;T2) for any fixed n and arbitrary rooted trees T1 ⊆ T2. We show that A(n;T ) is of the form ∑l j=0 qj(n)2 jn where...
متن کاملHighest Trees of Random Mappings
We prove the exact asymptotic 1 − Θ( 1 √ n ) for the probability that the underlying graph of a random mapping of n elements possesses a unique highest tree. The property of having a unique highest tree turned out to be crucial in the solution of the famous Road Coloring Problem [7] as well as in the proof of the author’s result about the probability of being synchronizable for a random automat...
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: 2020
ISSN: 0012-365X
DOI: 10.1016/j.disc.2020.111990