<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, we study the link between finite-dimensional Zinbiel algebras and combinatorial structures or (pseudo)digraphs determining which configurations are associated with those algebras. Some properties of Zinbiel algebras that can be read from their associated combinatorial structures are studied. We also analyze the isomorphism classes for each configuration associated with these algebras providing a new method to classify them and we compare our results with the current classifications of 2- and 3-dimensional Zinbiel algebras. We also obtain the 3-vertices combinatorial structures associated with such algebras. In order to complement the theoretical study, we have designed and performed the implementation of an algorithm which constructs and draws the (pseudo)digraph associated with a given Zinbiel algebra and, conversely, another procedure to test if a given combinatorial structure is associated with some Zinbiel algebra.</p>
</abstract>

In this paper, we study the link between finite-dimensional Zinbiel algebras and combinatorial structures or (pseudo)digraphs determining which configurations are associated with those algebras. Some properties of Zinbiel algebras that can be read from their associated combinatorial structures are studied. We also analyze the isomorphism classes for each configuration associated with these algebras providing a new method to classify them and we compare our results with the current classifications of 2- and 3-dimensional Zinbiel algebras. We also obtain the 3-vertices combinatorial structures associated with such algebras. In order to complement the theoretical study, we have designed and performed the implementation of an algorithm which constructs and draws the (pseudo)digraph associated with a given Zinbiel algebra and, conversely, another procedure to test if a given combinatorial structure is associated with some Zinbiel algebra.

Finite-dimensional Zinbiel algebras and combinatorial structures

Dpto. de Economía, Métodos Cuantitativos e Historia Económica

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Finite-dimensional Zinbiel algebras and combinatorial structures"}

In this paper, we study the link between finite-dimensional Zinbiel algebras and combinatorial structures or (pseudo)digraphs determining which configurations...

Finite-dimensional Zinbiel algebras and combinatorial structures

Published Online: Oct 08, 2022

Page range: 67 - 96

Received: Nov 02, 2021

Accepted: Jan 30, 2022

DOI: https://doi.org/10.2478/auom-2022-0035

Keywords
Graph, combinatorial structure, Zinbiel algebra, algorithm, complexity

© 2022 Manuel Ceballos et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Finite-dimensional Zinbiel algebras and combinatorial structures

Published Online: Oct 08, 2022

Page range: 67 - 96

Received: Nov 02, 2021

Accepted: Jan 30, 2022

DOI: https://doi.org/10.2478/auom-2022-0035

KeywordsGraph, combinatorial structure, Zinbiel algebra, algorithm, complexity

© 2022 Manuel Ceballos et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Graph, combinatorial structure, Zinbiel algebra, algorithm, complexity