Amenability and non-uniform growth of some directed automorphism groups of a rooted tree

This note deals with a formula due to G. Labelle for the summed cycle indices of all rooted trees, which resembles the well-known formula for the cycle index of the symmetric group in some way. An elementary proof is provided as well as some immediate corollaries and applications, in particular a new application to the enumeration of $k$-decomposable trees. A tree is called $k$-decomposable in this context if it has a spanning forest whose components are all of size $k$.

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CONJUGATION IN TREE AUTOMORPHISM GROUPS

International Journal of Algebra and Computation ◽

10.1142/s021819670100070x ◽

2001 ◽

Vol 11 (05) ◽

pp. 529-547 ◽

Cited By ~ 18

Author(s):

PIOTR W. GAWRON ◽

VOLODYMYR V. NEKRASHEVYCH ◽

VITALY I. SUSHCHANSKY

Keyword(s):

Automorphism Group ◽

Automorphism Groups ◽

Rooted Tree ◽

Symmetric Groups ◽

Wreath Products ◽

Rooted Trees ◽

Full Description ◽

Finite Tree ◽

Locally Finite ◽

Infinite Sequences

It is given a full description of conjugacy classes in the automorphism group of the locally finite tree and of a rooted tree. They are characterized by their types (a labeled rooted trees) similar to the cyclical types of permutations. We discuss separately the case of a level homogenous tree, i.e. conjugality in wreath products of infinite sequences of symmetric groups. It is proved those automorphism groups of rooted and homogenous non-rooted trees are ambivalent.

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Holomorphic Automorphism Groups in Banach Spaces: An Elementary Introduction

10.1016/s0304-0208(08)x7042-2 ◽

1985 ◽

Keyword(s):

Banach Spaces ◽

Automorphism Groups ◽

Holomorphic Automorphism ◽

Holomorphic Automorphism Groups

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HTPC: heterogeneous traffic-aware partition coding for random packet spraying in data center networks

Journal of Cloud Computing Advances Systems and Applications ◽

10.1186/s13677-021-00248-4 ◽

2021 ◽

Vol 10 (1) ◽

Author(s):

Jiawei Huang ◽

Shiqi Wang ◽

Shuping Li ◽

Shaojun Zou ◽

Jinbin Hu ◽

...

Keyword(s):

Data Center ◽

Large Scale ◽

Network Performance ◽

Rooted Tree ◽

Heterogeneous Traffic ◽

Data Center Networks ◽

Packet Reordering ◽

Traffic Characteristics ◽

Network Utilization ◽

The Impact

AbstractModern data center networks typically adopt multi-rooted tree topologies such leaf-spine and fat-tree to provide high bisection bandwidth. Load balancing is critical to achieve low latency and high throughput. Although the per-packet schemes such as Random Packet Spraying (RPS) can achieve high network utilization and near-optimal tail latency in symmetric topologies, they are prone to cause significant packet reordering and degrade the network performance. Moreover, some coding-based schemes are proposed to alleviate the problem of packet reordering and loss. Unfortunately, these schemes ignore the traffic characteristics of data center network and cannot achieve good network performance. In this paper, we propose a Heterogeneous Traffic-aware Partition Coding named HTPC to eliminate the impact of packet reordering and improve the performance of short and long flows. HTPC smoothly adjusts the number of redundant packets based on the multi-path congestion information and the traffic characteristics so that the tailing probability of short flows and the timeout probability of long flows can be reduced. Through a series of large-scale NS2 simulations, we demonstrate that HTPC reduces average flow completion time by up to 60% compared with the state-of-the-art mechanisms.

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Pentavalent 1-Transitive Digraphs with Non-Solvable Automorphism Groups

Indian Journal of Pure and Applied Mathematics ◽

10.1007/s13226-020-0504-7 ◽

2020 ◽

Vol 51 (4) ◽

pp. 1919-1930

Author(s):

Masoumeh Akbarizadeh ◽

Mehdi Alaeiyan ◽

Raffaele Scapellato

Keyword(s):

Automorphism Groups

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Hierarchical Analysis of Nucleotide Diversity in Geographically Structured Populations

Genetics ◽

10.1093/genetics/142.2.629 ◽

1996 ◽

Vol 142 (2) ◽

pp. 629-639 ◽

Cited By ~ 4

Author(s):

Kent E Holsinger ◽

Roberta J Mason-Gamer

Keyword(s):

Nucleotide Diversity ◽

Restriction Site ◽

Rooted Tree ◽

Structured Populations ◽

Hierarchical Analysis ◽

Restriction Site Variation ◽

Hierarchical Levels ◽

Site Variation ◽

The Mean ◽

Mean Time

Abstract Existing methods for analyzing nucleotide diversity require investigators to identify relevant hierarchical levels before beginning the analysis. We describe a method that partitions diversity into hierarchical components while allowing any structure present in the data to emerge naturally. We present an unbiased version of Nei's nucleotide diversity statistics and show that our modification has the same properties as Wright's F ST. We compare its statistical properties with several other F ST estimators, and we describe how to use these statistics to produce a rooted tree of relationships among the sampled populations in which the mean time to coalescence of haplotypes drawn from populations belonging to the same node is smaller than the mean time to coalescence of haplotypes drawn from populations belonging to different nodes. We illustrate the method by applying it to data from a recent survey of restriction site variation in the chloroplast genome of Coreopsis grandiflora.

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Automorphism groups of Hadamard matrices

Journal of Combinatorial Theory ◽

10.1016/s0021-9800(69)80088-8 ◽

1969 ◽

Vol 6 (3) ◽

pp. 279-281 ◽

Cited By ~ 24

Author(s):

William M. Kantor

Keyword(s):

Automorphism Groups ◽

Hadamard Matrices

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Serre’s Property (FA) for automorphism groups of free products

Journal of Group Theory ◽

10.1515/jgth-2019-0140 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Naomi Andrew

Keyword(s):

Automorphism Group ◽

Free Product ◽

Finite Groups ◽

Automorphism Groups ◽

Sufficient Conditions ◽

Free Products ◽

Cyclic Groups ◽

Link Type ◽

Open Case

AbstractWe provide some necessary and some sufficient conditions for the automorphism group of a free product of (freely indecomposable, not infinite cyclic) groups to have Property (FA). The additional sufficient conditions are all met by finite groups, and so this case is fully characterised. Therefore, this paper generalises the work of N. Leder [Serre’s Property FA for automorphism groups of free products, preprint (2018), https://arxiv.org/abs/1810.06287v1]. for finite cyclic groups, as well as resolving the open case of that paper.

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