Graphical representations of cyclic permutation groups

2020 ◽  
Vol 277 ◽  
pp. 172-179
Author(s):  
Mariusz Grech ◽  
Andrzej Kisielewicz
Keyword(s):  
Cyclic Permutation ◽  
Permutation Groups ◽  
Graphical Representations

scholarly journals Graphical cyclic permutation groups

2014 ◽  
Vol 337 ◽  
pp. 25-33 ◽  
Author(s):  
Mariusz Grech
Keyword(s):  
Cyclic Permutation ◽  
Permutation Groups

scholarly journals Abelian permutation groups with graphical representations

2021 ◽  
Author(s):  
Mariusz Grech ◽  
Andrzej Kisielewicz
Keyword(s):  
Permutation Group ◽  
Automorphism Groups ◽  
Permutation Groups ◽  
Graphical Representations ◽  
Colored Graphs

AbstractIn this paper we characterize those automorphism groups of colored graphs and digraphs that are abelian as abstract groups. This is done in terms of basic permutation group properties. Using Schur’s classical terminology, what we provide is characterizations of the classes of 2-closed and $$2^*$$ 2 ∗ -closed abelian permutation groups. This is the first characterization concerning these classes since they were defined.

scholarly journals Cyclic Permutation Groups that are Automorphism Groups of Graphs

2019 ◽  
Vol 35 (6) ◽  
pp. 1405-1432 ◽  
Author(s):  
Mariusz Grech ◽  
Andrzej Kisielewicz
Keyword(s):  
Automorphism Group ◽  
Permutation Group ◽  
Boolean Functions ◽  
Automorphism Groups ◽  
Cyclic Permutation ◽  
Permutation Groups ◽  
Symmetry Groups ◽  
Cyclic Groups

Abstract In this paper we establish conditions for a permutation group generated by a single permutation to be an automorphism group of a graph. This solves the so called concrete version of König’s problem for the case of cyclic groups. We establish also similar conditions for the symmetry groups of other related structures: digraphs, supergraphs, and boolean functions.

scholarly journals Graphical cyclic permutation groups

1981 ◽  
pp. 339-346 ◽  
Author(s):  
S. P. Mohanty ◽  
M. R. Sridharan ◽  
S. K. Shukla
Keyword(s):  
Cyclic Permutation ◽  
Permutation Groups

scholarly journals Permutation Polytopes of Cyclic Groups

2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Barbara Baumeister ◽  
Christian Haase ◽  
Benjamin Nill ◽  
Andreas Paffenholz
Keyword(s):  
Large Class ◽  
Cyclic Permutation ◽  
Permutation Groups ◽  
Convex Hulls ◽  
Facet Structure ◽  
Cyclic Groups ◽  
Permutation Matrices ◽  
Il Y A ◽  
International Audience ◽  
Permutation Polytope

International audience We investigate the combinatorics and geometry of permutation polytopes associated to cyclic permutation groups, i.e., the convex hulls of cyclic groups of permutation matrices. In the situation that the generator of the group consists of at most two orbits, we can give a complete combinatorial description of the associated permutation polytope. In the case of three orbits the facet structure is already quite complex. For a large class of examples we show that there exist exponentially many facets. Nous ètudions les propriètès combinatoires et gèomètriques des polytopes de permutations pour des groupes cycliques. C'est à dire, donnè un groupe cyclique de matrices de permutations, nous considèrons son enveloppe convexe. Si le gènèrateur du groupe possède un ou deux orbites il y a une dèscription simple du polytope. Par contre, le cas de trois (ou plus) orbites est beaucoup plus compliquè. Pour une classe ample d'examples nous construisons un nombre exponentiel de faces de co-dimension un.

Compact cellular algebras and permutation groups

1999 ◽  
Vol 197-198 (1-3) ◽  
pp. 247-267 ◽  
Author(s):  
S Evdokimov
Keyword(s):  
Permutation Groups ◽  
Cellular Algebras

Visualization of Enneper’s surface by line graphics

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 387-405 ◽  
Author(s):  
Vesna Velickovic
Keyword(s):  
Minimal Surface ◽  
Graphical Representations ◽  
Lines Of Curvature ◽  
Geodesic Lines

Here we study Enneper?s minimal surface and some of its properties. We compute and visualize the lines of self-intersection, lines of intersections with planes, lines of curvature, asymptotic and geodesic lines of Enneper?s surface. For the graphical representations of all the results we use our own software for line graphics.

Proof Theory of the Cut Rule

2018 ◽  
Author(s):  
J. R. B. Cockett ◽  
R. A. G. Seely
Keyword(s):  
Proof Theory ◽  
Graphical Representation ◽  
Basic Component ◽  
Graphical Representations ◽  
Mathematical Language ◽  
Basic Logic ◽  
Cut Rule ◽  
Structural Rules ◽  
The One ◽  
Categorical Semantics

This chapter describes the categorical proof theory of the cut rule, a very basic component of any sequent-style presentation of a logic, assuming a minimum of structural rules and connectives, in fact, starting with none. It is shown how logical features can be added to this basic logic in a modular fashion, at each stage showing the appropriate corresponding categorical semantics of the proof theory, starting with multicategories, and moving to linearly distributive categories and *-autonomous categories. A key tool is the use of graphical representations of proofs (“proof circuits”) to represent formal derivations in these logics. This is a powerful symbolism, which on the one hand is a formal mathematical language, but crucially, at the same time, has an intuitive graphical representation.

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