volume 28, issue 2, P123-150 2002
DOI: 10.1007/s00454-002-0727-x
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Abstract: ABSTRACTWe derive improved bounds on the number of fc-dimensional simplices spanned by a set of n points in R'^ that are congruent to a given fc-simplex, for fc < d -1. Let f^ '{n) be the maximum number of fc-simplices spanned by a set of n points in R"* that are congruent to a given fc-simplex. We prove that /j (n) = 0("5/3 .20(a^(n)))_ y(4)(") ^ 0{n^+n, A^\n) = 0(n^/3), and /^^'(n) = 0(TI^/**+^). We also derive a recurrence to bound fjf'^ (n) for arbitrary values of k and d, and use it to derive the bound f…

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