The Number of M-Sequences and f-Vectors

M

-sequences (a.k.a. f-vectors for multicomplexes or O-sequences) in terms of the number of variables and a maximum degree. In particular, it is shown that the number of M-sequences for at most 2 variables are powers of two and for at most 3 variables are Bell numbers. We give an asymptotic estimate of the number of M-sequences when the number of variables is fixed. This leads to a new lower bound for the number of polytopes with few vertices. We also prove a similar recursive formula for the number of f-vectors for simplicial complexes. Keeping the maximum degree fixed we get the number of M-sequences and the number of f-vectors for simplicial complexes as polynomials in the number of variables and it is shown that these numbers are asymptotically equal.

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Received: February 28, 1996/Revised: February 26, 1998

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Linusson, S. The Number of M-Sequences and f-Vectors. Combinatorica 19, 255–266 (1999). https://doi.org/10.1007/s004930050055

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  • AMS Subject Classification (1991) Classes:  05A15; 52B05, 05A16