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The Matroid Union | A blog for and by the matroid community The Matroid Union A blog for and by the matroid community Search Main menu Skip to primary content Skip to secondary content Home About Talks Meetings Q&A Post navigation ← Older posts A theory of q-transversals Posted on June 2, 2025 by Guest Contributor Reply This is a guest post by Mark Saaltink . A $q$-analog is formed by replacing the notion of a set by the notion of a vector space, with a corresponding replacement of other concepts: cardinality becomes dimension, elements are replaced by 1-dimensional subspaces, the empty set is replaced by the 0-dimensional subspace, intersection remains the same, and union is replaced by sum. (It is not always clear how to replace set difference or symmetric difference.) The application of this idea to matroid theory gives the theory of q -matroids [Jur2018][Cer2022], which Relinde Jurrius has described in this forum, most recently with th...
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