Math 669: Combinatorics of Polytopes
نویسنده
چکیده
These are rather condensed notes, not really proofread or edited, presenting key definitions and results of the course that I taught in Winter 2010 term. Problems marked by ◦ are easy and basic, problems marked by ∗ may be difficult. Typeset by AMS-TEX 1
منابع مشابه
On the number of faces of centrally-symmetric simplicial polytopes
I. Bfirfiny and L. Lovfisz [Acta Math. Acad. Sci. Hung. 40, 323-329 (1982)] showed that a d-dimensional centrally-symmetric simplicial polytope ~ has at least 2 d facets, and conjectured a lower bound for the number f~ of i-dimensional faces o f ~ in terms ofd and the number f0 = 2n of d vertices. Define integers ho . . . . . he by Z f~-1(x 1) d-' = ~ hi xd-'. A. Bj6rner conjectured (uni=O i=O ...
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Let n be a positive integer. We may write (or split) n as sums of n nonincreasing nonnegative integers p1, p2, . . . , pn in different ways (or partitions; see Section 2). For example, 3 = 3 + 0 + 0 = 2 + 1 + 0 = 1 + 1 + 1. If we denote by P (n) the number of different partitions of n, then P (3) = 3. One may check that P (5) = 7. As n gets large, P (n) increases rapidly. It is astounding that ...
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