On Point-Symmetric Tournaments

1970 ◽  
Vol 13 (3) ◽  
pp. 317-323 ◽  
Author(s):  
Brian Alspach
Keyword(s):  
Automorphism Group ◽  
Directed Graph ◽  
Combinatorial Argument ◽  
Maximum Value ◽  
Equality Holding

A tournament is a directed graph in which there is exactly one arc between any two distinct vertices. Let denote the automorphism group of T. A tournament T is said to be point-symmetric if acts transitively on the vertices of T. Let g(n) be the maximum value of taken over all tournaments of order n. In [3] Goldberg and Moon conjectured that with equality holding if and only if n is a power of 3. The case of point-symmetric tournaments is what prevented them from proving their conjecture. In [2] the conjecture was proved through the use of a lengthy combinatorial argument involving the structure of point-symmetric tournaments. The results in this paper are an outgrowth of an attempt to characterize point-symmetric tournaments so as to simplify the proof employed in [2].

scholarly journals Quantum Symmetries of Graph C*-algebras

2018 ◽  
Vol 61 (4) ◽  
pp. 848-864 ◽  
Author(s):  
Simon Schmidt ◽  
Moritz Weber
Keyword(s):  
Automorphism Group ◽  
Directed Graph ◽  
Operator Algebras ◽  
Automorphism Groups ◽  
Undirected Graphs ◽  
C Algebras ◽  
Quantum Symmetry ◽  
Quantum Symmetries ◽  
Multiple Edges ◽  
Definition Of

AbstractThe study of graph C*-algebras has a long history in operator algebras. Surprisingly, their quantum symmetries have not yet been computed. We close this gap by proving that the quantum automorphism group of a finite, directed graph without multiple edges acts maximally on the corresponding graph C*-algebra. This shows that the quantum symmetry of a graph coincides with the quantum symmetry of the graph C*-algebra. In our result, we use the definition of quantum automorphism groups of graphs as given by Banica in 2005. Note that Bichon gave a different definition in 2003; our action is inspired from his work. We review and compare these two definitions and we give a complete table of quantum automorphism groups (with respect to either of the two definitions) for undirected graphs on four vertices.

scholarly journals Finite Factors of Bernoulli Schemes and Distinguishing Labelings of Directed Graphs

10.37236/6 ◽  
2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Andrew Lazowski ◽  
Stephen M. Shea
Keyword(s):  
Automorphism Group ◽  
Lower Bound ◽  
Directed Graph ◽  
Directed Graphs ◽  
Bell Numbers ◽  
Undirected Graphs ◽  
Bernoulli Scheme ◽  
Finite Set ◽  
Finite Factor

A labeling of a graph is a function from the vertices of the graph to some finite set.  In 1996, Albertson and Collins defined distinguishing labelings of undirected graphs.  Their definition easily extends to directed graphs.  Let $G$ be a directed graph associated to the $k$-block presentation of a Bernoulli scheme $X$.  We determine the automorphism group of $G$, and thus the distinguishing labelings of $G$.  A labeling of $G$ defines a finite factor of $X$.  We define demarcating labelings and prove that demarcating labelings define finitarily Markovian finite factors of $X$.  We use the Bell numbers to find a lower bound for the number of finitarily Markovian finite factors of a Bernoulli scheme.  We show that demarcating labelings of $G$ are distinguishing.

scholarly journals Automorphism groups of countable algebraically closed graphs and endomorphisms of the random graph

2016 ◽  
Vol 160 (3) ◽  
pp. 437-462 ◽  
Author(s):  
IGOR DOLINKA ◽  
ROBERT D. GRAY ◽  
JILLIAN D. McPHEE ◽  
JAMES D. MITCHELL ◽  
MARTYN QUICK
Keyword(s):  
Automorphism Group ◽  
Bipartite Graph ◽  
Random Graph ◽  
Directed Graph ◽  
Automorphism Groups ◽  
Structural Information ◽  
Maximal Subgroups ◽  
Endomorphism Monoid

AbstractWe establish links between countable algebraically closed graphs and the endomorphisms of the countable universal graph R. As a consequence we show that, for any countable graph Γ, there are uncountably many maximal subgroups of the endomorphism monoid of R isomorphic to the automorphism group of Γ. Further structural information about End R is established including that Aut Γ arises in uncountably many ways as a Schützenberger group. Similar results are proved for the countable universal directed graph and the countable universal bipartite graph.

scholarly journals AUTOMORPHISMS OF NONSELFADJOINT DIRECTED GRAPH OPERATOR ALGEBRAS

2009 ◽  
Vol 87 (2) ◽  
pp. 175-196
Author(s):  
BENTON L. DUNCAN
Keyword(s):  
Automorphism Group ◽  
Directed Graph ◽  
Maximal Ideal ◽  
Operator Algebras ◽  
Maximal Ideal Space ◽  
Ideal Space ◽  
Normal Subgroups ◽  
Inner Automorphisms

AbstractWe analyze the automorphism group for the norm closed quiver algebras 𝒯+(Q). We begin by focusing on two normal subgroups of the automorphism group which are characterized by their actions on the maximal ideal space of 𝒯+(Q). To further discuss arbitrary automorphisms we factor automorphism through subalgebras for which the automorphism group can be better understood. This allows us to classify a large number of noninner automorphisms. We suggest a candidate for the group of inner automorphisms.

scholarly journals Unique ergodicity of the automorphism group of the semigeneric directed graph

2021 ◽  
pp. 1-14
Author(s):  
COLIN JAHEL
Keyword(s):  
Automorphism Group ◽  
Directed Graph ◽  
Unique Ergodicity ◽  
Uniquely Ergodic

Abstract We prove that the automorphism group of the semigeneric directed graph (in the sense of Cherlin’s classification) is uniquely ergodic.

scholarly journals Quantum symmetry of graph C∗-algebras associated with connected graphs

2018 ◽  
Vol 21 (03) ◽  
pp. 1850019 ◽  
Author(s):  
Soumalya Joardar ◽  
Arnab Mandal
Keyword(s):  
Automorphism Group ◽  
Directed Graph ◽  
Automorphism Groups ◽  
Multiple Edge ◽  
Connected Graphs ◽  
C Algebras ◽  
Underlying Graph ◽  
Quantum Symmetry ◽  
Quantum Symmetries ◽  
Funct Anal

We define a notion of quantum automorphism groups of graph [Formula: see text]-algebras for finite, connected graphs. Under the assumption that the underlying graph does not have any multiple edge or loop, the quantum automorphism group of the underlying directed graph in the sense of Banica [Quantum automorphism groups of homogeneous graphs, J. Funct. Anal. 224 (2005) 243–280] (which is also the symmetry object in the sense of [S. Schmidt and M. Weber, Quantum symmetry of graph [Formula: see text]-algebras, arXiv:1706.08833 ] is shown to be a quantum subgroup of quantum automorphism group in our sense. Quantum symmetries for some concrete graph [Formula: see text]-algebras have been computed.

scholarly journals Holomorphic mappings into a compact quotient of symmetric bounded domain

1976 ◽  
Vol 64 ◽  
pp. 159-175 ◽  
Author(s):  
Toshikazu Sunada
Keyword(s):  
Automorphism Group ◽  
Euclidean Space ◽  
Bounded Domain ◽  
Discrete Subgroup ◽  
Holomorphic Mappings ◽  
Finiteness Property ◽  
Maximum Value ◽  
Compact Quotient ◽  
Complex Euclidean Space ◽  
Torsion Free

In this paper, we shall be concerned with the finiteness property of certain holomorphic mappings into a compact quotient of symmetric bounded domain.Let be a symmetric bounded domain in n-dimensional complex Euclidean space Cn and Γ\ be a compact quotient of S by a torsion free discrete subgroup Γ of automorphism group of . Further, we denote by l() the maximum value of dimension of proper boundary component of , which is less than n (=dim).

A Combinatorial Proof of a Conjecture of Goldberg and Moon

1968 ◽  
Vol 11 (5) ◽  
pp. 655-661 ◽  
Author(s):  
Brian Alspach
Keyword(s):  
Automorphism Group ◽  
Symmetric Group ◽  
Combinatorial Proof ◽  
Odd Order ◽  
Equality Holding

Let Tn denote a tournament of order n, let G(Tn) denote the automorphism group of Tn, let |G| denote the order of the group G, and let g(n) denote the maximum of |G(Tn)| taken over all tournaments Tn of order n. Goldberg and Moon conjectured [2] that for all n≥1 with equality holding if and only if n is a power of 3. In an addendum to [2] it was pointed out that their conjecture is equivalent to the conjecture that if G is any odd order subgroup of Sn, the symmetric group of degree n, then with equality possible if and only if n is a power of 3. The latter conjecture was proved in [1] by John D. Dixon who made use of the Feit-Thompson theorem in his proof. In this paper we avoid use of the Feit-Thompson result and give a combinatorial proof of the Goldberg-Moon conjecture.

scholarly journals AUTOMORPHISMS OF METABELIAN PRIME POWER ORDER GROUPS OF MAXIMAL CLASS

2008 ◽  
Vol 77 (2) ◽  
pp. 261-276
Author(s):  
S. FOULADI ◽  
R. ORFI
Keyword(s):  
Automorphism Group ◽  
Prime Power ◽  
Structure Theorem ◽  
Maximal Class ◽  
Prime Power Order ◽  
Full Automorphism Group ◽  
Maximum Value

AbstractLet G be a p-group of maximal class of order pn. It is shown that the order of the group of all automorphisms of G centralizing the Frattini quotient takes the maximum value p2n−4 if and only if G is metabelian. A structure theorem is proved for the Sylow p-subgroup, Autp(G), of the automorphism group of G when G is metabelian. For p=2, Aut2(G) is the full automorphism group of G. For p=3, we prove a structure theorem for the full automorphism group of G.

Prothrombin Evaluation as Obtained by Kinetics Studies of Antigen-Antibody Reaction in a Laser Nephelometer

1984 ◽  
Vol 52 (01) ◽  
pp. 015-018 ◽  
Author(s):  
A Girolami ◽  
A Sticchi ◽  
R Melizzi ◽  
L Saggin ◽  
G Ruzza
Keyword(s):  
Liver Cirrhosis ◽  
Cirrhotic Patient ◽  
Maximum Rate ◽  
Serum Proteins ◽  
Clotting Factors ◽  
Kinetics Studies ◽  
Maximum Value ◽  
Time Required ◽  
Antigen Antibody ◽  
Kinetics Of

SummaryLaser nephelometry is a technique which allows the evaluation of the concentration of several serum proteins and clotting factors. By means of this technique it is also possible to study the kinetics of the reaction between antigen and antibody. We studied the kinetics of the reaction between prothrombin and an antiprothrombin antiserum using several prothrombins namely: Prothrombin Padua, prothrombin Molise, which are two congenital dysprothrombinemias, cirrhotic, coumarin or normal prothrombins. Different behaviors in the kinetics of the reactions were shown even when the concentration of prothrombins was about the same in all plasma tested. These differences were analyzed by means of a computer (Apple II 48 RAM) programmed to solve four unknown equations (Rodbard’s equation). From the data so obtained one can see that when voltages at the beginning and at the end of the reaction are in all cases about the same, a clear difference in the time required to reach half the maximum value of the voltage can still be demonstrated. This parameter, which is expressed in minutes, is longer in coumarin and prothrombin Molise than in controls. On the contrary it is shorter in prothrombin Padua and has about the same value of controls in the cirrhotic patient. Moreover the time at which the maximum rate is obtained is longer in coumarin and prothrombin Molise than in controls and shorter in liver cirrhosis and prothrombin Padua. In conclusion data obtained show that coumarin prothrombin behaves in a different way from cirrhotic prothrombin and also that there is a different behaviour between the two congenital dysprothrombinemias.

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