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- W3150248522 abstract "In this paper, we introduce higher symmetric simplicial complexity $SC_n^{Sigma}(K)$ of a simplicial complex $K$ and higher symmetric combinatorial complexity $CC_n^{Sigma}(P)$ of a finite poset $P$. These are simplicial and combinatorial approaches to symmetric motion planning of Basabe - Gonz'{a}lez - Rudyak - Tamaki. We prove that the symmetric simplicial complexity $SC_n^{Sigma}(K)$ is equal to symmetric topological complexity $TC_n^{Sigma}(|K|)$ of the geometric realization of $K$ and the symmetric combinatorial complexity $CC_n^{Sigma}(P)$ is equal to symmetric topological complexity $TC_n^{Sigma}(|mathcal{K}(P)|)$ of the geometric realization of the order complex of $P$." @default.
- W3150248522 created "2021-04-13" @default.
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- W3150248522 date "2023-05-01" @default.
- W3150248522 modified "2023-10-18" @default.
- W3150248522 title "Simplicial and combinatorial versions of higher symmetric topological complexity" @default.
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- W3150248522 doi "https://doi.org/10.1016/j.topol.2023.108491" @default.
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