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- W2166736885 abstract "For classes ${cal O}$ of structures on finite linear orders (permutations, ordered graphs etc.) endowed with containment order $preceq$ (containment of permutations, subgraph relation etc.), we investigate restrictions on the function $f(n)$ counting objects with size $n$ in a lower ideal in $({cal O},preceq)$. We present a framework of edge $P$-colored complete graphs $({cal C}(P),preceq)$ which includes many of these situations, and we prove for it two such restrictions (jumps in growth): $f(n)$ is eventually constant or $f(n)ge n$ for all $nge 1$; $f(n)le n^c$ for all $nge 1$ for a constant $c>0$ or $f(n)ge F_n$ for all $nge 1$, $F_n$ being the Fibonacci numbers. This generalizes a fragment of a more detailed theorem of Balogh, Bollobás and Morris on hereditary properties of ordered graphs." @default.
- W2166736885 created "2016-06-24" @default.
- W2166736885 creator A5005859787 @default.
- W2166736885 date "2008-05-31" @default.
- W2166736885 modified "2023-09-28" @default.
- W2166736885 title "On Growth Rates of Permutations, Set Partitions, Ordered Graphs and Other Objects" @default.
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- W2166736885 doi "https://doi.org/10.37236/799" @default.
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