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- W1978167511 abstract "Consider the question: Given integers 0 le k N(d,k) the answer is yes if and only if {G(d,k)} divides n . Furthermore, a formula for G(d,k) is given, showing that, e.g., G(d,k)=1 if $k ge leftlfloor (d+1)/{2}rightrfloor$ or if both d and k are even, and also in some other cases (meaning that all numbers beyond N(d,k) occur as the number of k -faces of some simple d -polytope).This question has previously been studied only for the case of vertices (k=0 ), where Lee [Le] proved the existence of N(d,0) (with G(d,0)=1 or 2 depending on whether d is even or odd), and Prabhu [P1] showed that $N(d,0) le cdsqrt {d}$. We show here that asymptotically the true value of Prabhu's constant is $c=sqrt2 $ if d is even, and c=1 if d is odd." @default.
- W1978167511 created "2016-06-24" @default.
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- W1978167511 date "2007-07-01" @default.
- W1978167511 modified "2023-10-01" @default.
- W1978167511 title "The Number of k-Faces of a Simple d-Polytope" @default.
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- W1978167511 doi "https://doi.org/10.1007/s00454-007-0382-3" @default.
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