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- W4368755096 abstract "We define a certain merging operation that given two $d$-polytopes $P$ and $Q$ such that $P$ has a simplex facet $F$ and $Q$ has a simple vertex $v$ produces a new $d$-polytope $Phspace{0.1em}triangleright Q$ with $f_0(P)+f_0(Q)-(d+1)$ vertices. We show that if for some $1leq ileq d-1$, $P$ and $Q$ are $(d-i)$-simplicial $i$-simple $d$-polytopes, then so is $Phspace{0.1em}triangleright Q$. We then use this operation to construct new families of $(d-i)$-simplicial $i$-simple $d$-polytopes. Specifically, we prove that for all $2leq i leq d-2leq 6$ with the exception of $(i,d)=(3,8)$ and $(5,8)$, there is an infinite family of $(d-i)$-simplicial $i$-simple $d$-polytopes; furthermore, for all $2leq ileq 4$, there is an infinite family of self-dual $i$-simplicial $i$-simple $2i$-polytopes. Finally, we show that for any $dgeq 4$, there are $2^{Omega(N)}$ combinatorial types of $(d-2)$-simplicial $2$-simple $d$-polytopes with at most $N$ vertices." @default.
- W4368755096 created "2023-05-05" @default.
- W4368755096 creator A5000152196 @default.
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- W4368755096 date "2023-05-02" @default.
- W4368755096 modified "2023-09-30" @default.
- W4368755096 title "The merging operation and $(d-i)$-simplicial $i$-simple $d$-polytopes" @default.
- W4368755096 doi "https://doi.org/10.48550/arxiv.2305.01829" @default.
- W4368755096 hasPublicationYear "2023" @default.
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