A theory of $q$-transversals
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917958528270336 |
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| author | Saaltink, Mark |
| author_facet | Saaltink, Mark |
| contents | Given an indexed family ${\cal A} = (A_1, A_2, \dotsc, A_n)$ of subsets of some given set $S$, a \emph{transversal} is a set of distinct elements $x_1, x_2, \dotsc, x_n$ with each $x_i \in A_i$. Transversals have been studied since 1935 and have many attractive properties, with a deep connection to matroids. 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. In this paper we define a $q$-analog of the theory of transversals, and show that many of the main properties of ordinary transversals are shared by this analog. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12201 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A theory of $q$-transversals Saaltink, Mark Combinatorics 05B35, 05A30 Given an indexed family ${\cal A} = (A_1, A_2, \dotsc, A_n)$ of subsets of some given set $S$, a \emph{transversal} is a set of distinct elements $x_1, x_2, \dotsc, x_n$ with each $x_i \in A_i$. Transversals have been studied since 1935 and have many attractive properties, with a deep connection to matroids. 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. In this paper we define a $q$-analog of the theory of transversals, and show that many of the main properties of ordinary transversals are shared by this analog. |
| title | A theory of $q$-transversals |
| topic | Combinatorics 05B35, 05A30 |
| url | https://arxiv.org/abs/2503.12201 |