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- W4300522045 abstract "The growth-rate function for a minor-closed class $mathcal{M}$ of matroids is the function $h$ where, for each non-negative integer $r$, $h(r)$ is the maximum number of elements of a simple matroid in $mathcal{M}$ with rank at most $r$. The Growth-Rate Theorem of Geelen, Kabell, Kung, and Whittle shows, essentially, that the growth-rate function is always either linear, quadratic, exponential, or infinite. Morover, if the growth-rate function is quadratic, then $h(r)ge binom{r+1}{2}$, with the lower bound coming from the fact that such classes necessarily contain all graphic matroids. We characterise the classes that satisfy $h(r) = binom{r+1}{2}$ for all sufficiently large $r$." @default.
- W4300522045 created "2022-10-03" @default.
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- W4300522045 date "2014-09-02" @default.
- W4300522045 modified "2023-09-26" @default.
- W4300522045 title "Matroids denser than a clique" @default.
- W4300522045 doi "https://doi.org/10.48550/arxiv.1409.0777" @default.
- W4300522045 hasPublicationYear "2014" @default.
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