The direct sum of q-matroids

For classical matroids, the direct sum is one of the most straightforward methods to make a new matroid out of existing ones. This paper defines a direct sum for q -matroids, the q -analogue of matroids. This is a lot less straightforward than in the classical case, as we will try to convince the re...

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Bibliographic Details
Published inJournal of algebraic combinatorics Vol. 59; no. 2; pp. 291 - 330
Main Authors Ceria, Michela, Jurrius, Relinde
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2024
Springer Nature B.V
Subjects
Boolean
Circuits
Combinatorics
Computer Science
Convex and Discrete Geometry
Group Theory and Generalizations
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
05B35
analogue
05A30
Direct sum
matroid
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ISSN0925-9899
1572-9192
1572-9192
DOI10.1007/s10801-023-01283-x

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Summary:For classical matroids, the direct sum is one of the most straightforward methods to make a new matroid out of existing ones. This paper defines a direct sum for q -matroids, the q -analogue of matroids. This is a lot less straightforward than in the classical case, as we will try to convince the reader. With the use of submodular functions and the q -analogue of matroid union we come to a definition of the direct sum of q -matroids. As a motivation for this definition, we show it has some desirable properties.
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ISSN:0925-9899
1572-9192
1572-9192
DOI:10.1007/s10801-023-01283-x