1,720,967 research outputs found
The direct sum of q-matroids
Full text linkFor 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
Alternatives for the -matroid axioms of independent spaces, bases, and spanning spaces
Full text linkIt is well known that in q-matroids, axioms for independent spaces, bases,
and spanning spaces differ from the classical case of matroids, since the
straightforward q-analogue of the classical axioms does not give a q-matroid.
For this reason, a fourth axiom has been proposed. In this paper we show how we
can describe these spaces with only three axioms, providing two alternative
ways to do that. As an application, we show direct cryptomorphisms between
independent spaces and circuits and between independent spaces and bases.Comment: This version contains corrections to the published versio
Constructions of new q-cryptomorphisms
Full text linkIn the theory of classical matroids, there are several known equivalent axiomatic systems that define a matroid, which are described as matroid cryptomorphisms. A q-matroid is a q-analogue of a matroid where subspaces play the role of the subsets in the classical theory. In this article we establish cryptomorphisms of q-matroids. In doing so we highlight the difference between classical theory and its q-analogue. We introduce a comprehensive set of q-matroid axiom systems and show cryptomorphisms between them and existing axiom systems of a q-matroid. These axioms are described as the rank, closure, basis, independence, dependence, circuit, hyperplane, flat, open space, spanning space, non-spanning space, and bi-colouring axioms
Weighted Subspace Designs from q-Polymatroids
Full text linkThe Assmus-Mattson Theorem gives a way to identify block designs arising from codes. This result was broadened to matroids and weighted designs by Britz et al. in 2009. In this work we present a further two-fold generalisation: first from matroids to polymatroids and also from sets to vector spaces. To achieve this, we study the characteristic polynomial of a q-polymatroid and outline several of its properties. We also derive a MacWilliams duality result and apply this to establish criteria on the weight enumerator of a q-polymatroid for which dependent spaces of the q-polymatroid form the blocks of a weighted subspace design
Constructions of New q-Cryptomorphisms
Full text linkInternational audienceIn the theory of classical matroids, there are several known equivalent axiomatic systems that define a matroid, which are described as matroid cryptomorphisms. A q-matroid is a q-analogue of a matroid where subspaces play the role of the subsets in the classical theory. In this article we establish cryptomorphisms of q-matroids. In doing so we highlight the difference between classical theory and its q-analogue. We introduce a comprehensive set of q-matroid axiom systems and show cryptomorphisms between them and existing axiom systems of a q-matroid. These axioms are described as the rank, closure, basis, independence, dependence, circuit, hyperplane, flat, open space, spanning space, non-spanning space, and bi-colouring axioms
The extended and generalized rank weight enumerator
No full textNon UBCUnreviewedAuthor affiliation: University of NeuchâtelPostdoctora
The direct sum of -matroids
Full text linkFor 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 -matroids, the -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 -analogue of matroid
union we come to a definition of the direct sum of -matroids. As a
motivation for this definition, we show it has some desirable properties
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
A q-analogue of delta-matroids and related concepts
Full text linkWe define and study q-delta-matroids, and q-g-matroids. These objects are
analogues, for finite-dimensional vector spaces over finite fields, of
delta-matroids and g-matroids arising from finite sets. We compare axiomatic
descriptions with definitions by means of strong maps of q-matroids
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