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446,997
DISTANCES BETWEEN ROOTED TREES
, 1989
"... Summary. Two types of a distance between isomorphism classes of graphs are adapted for rooted trees. ..."
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Summary. Two types of a distance between isomorphism classes of graphs are adapted for rooted trees.
On the Hopf Algebra of Rooted Trees
, 710
"... We find a formula to compute the number of the generators, which generate the nfiltered space of Hopf algebra of rooted trees, i.e. the number of equivalent classes of rooted trees with weight n. Applying Hopf algebra of rooted trees, we show that the analogue of Andruskiewitsch and Schneider’s Con ..."
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We find a formula to compute the number of the generators, which generate the nfiltered space of Hopf algebra of rooted trees, i.e. the number of equivalent classes of rooted trees with weight n. Applying Hopf algebra of rooted trees, we show that the analogue of Andruskiewitsch and Schneider’s
Combinatorics of rooted trees and Hopf algebras
, 2002
"... We begin by considering the graded vector space with a basis consisting of rooted trees, with grading given by the count of nonroot vertices. We define two linear operators on this vector space, the growth and pruning operators, which respectively raise and lower grading; their commutator is the op ..."
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Cited by 40 (5 self)
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We begin by considering the graded vector space with a basis consisting of rooted trees, with grading given by the count of nonroot vertices. We define two linear operators on this vector space, the growth and pruning operators, which respectively raise and lower grading; their commutator
Rooted Tree and Spanning Tree Constraints
"... 1 Introduction We present two specialised/nary constraints for modelling trees. Our first constraint allows for the modelling of rooted trees. In this model constrained integer ..."
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1 Introduction We present two specialised/nary constraints for modelling trees. Our first constraint allows for the modelling of rooted trees. In this model constrained integer
The enumeration of rooted trees by total height
 J. of the Aust. Math. Soc
, 1969
"... The height (as in [3] and [4]) of a point in a rooted tree is the length of the path (that is, the number of lines in the path) from it to the root; the total height of a rooted tree is the sum of the heights of its points. The latter arises naturally in studies of random neural networks made by one ..."
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Cited by 11 (0 self)
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The height (as in [3] and [4]) of a point in a rooted tree is the length of the path (that is, the number of lines in the path) from it to the root; the total height of a rooted tree is the sum of the heights of its points. The latter arises naturally in studies of random neural networks made
Random Walks on Rooted Trees
"... For arbitrary positive integers h and m, we consider the family of all rooted trees of height h having exactly m vertices at distance h from the root. We refer to such trees as (h, m)trees. For a tree T from this family, we consider a simple random walk on T which starts at the root and terminates ..."
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For arbitrary positive integers h and m, we consider the family of all rooted trees of height h having exactly m vertices at distance h from the root. We refer to such trees as (h, m)trees. For a tree T from this family, we consider a simple random walk on T which starts at the root and terminates
On Balloon Drawings of Rooted Trees
 Proc. 13th International Symposium on Graph Drawing (GD’05
, 2005
"... Among various styles of tree drawing reported in the literature, balloon drawing enjoys a desirable feature of displaying tree structures in a rather balanced fashion. Each subtree in the balloon drawing of a tree is enclosed in a circle. Along any path from the root node, the radius of each circle ..."
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Cited by 12 (1 self)
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Among various styles of tree drawing reported in the literature, balloon drawing enjoys a desirable feature of displaying tree structures in a rather balanced fashion. Each subtree in the balloon drawing of a tree is enclosed in a circle. Along any path from the root node, the radius of each circle
A DATA STRUCTURE FOR DYNAMICALLY MAINTAINING ROOTED TREES
, 1992
"... A data structure for dynamically maintaining rooted trees ..."
PreLie algebras and the rooted trees operad
 Internat. Math. Res. Notices
"... Abstract. A preLie algebra is a vector space L endowed with a bilinear product · : L × L → L satisfying the relation (x · y) · z − x · (y · z) = (x · z) · y − x · (z · y), ∀x, y, z ∈ L. We give an explicit combinatorial description in terms of rooted trees of the operad associated to this type o ..."
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Cited by 113 (20 self)
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Abstract. A preLie algebra is a vector space L endowed with a bilinear product · : L × L → L satisfying the relation (x · y) · z − x · (y · z) = (x · z) · y − x · (z · y), ∀x, y, z ∈ L. We give an explicit combinatorial description in terms of rooted trees of the operad associated to this type
Results 1  10
of
446,997