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We show that symmetric Venn diagrams for n sets exist for every prime n, settling an open question. Until this time, n = 11 was the largest prime for which the existence of such diagrams had been proven, a result of Peter Hamburger. We show that the problem can be reduced to finding a symmetric chain decomposition, satisfying a certain cover property, in a… (More)

An n-bit Gray code is a circular listing of the 2 n n-bit strings so that successive strings differ only in one bit position. An n-bit antipodal Gray code has the additional property that the complement of any string appears exactly n steps away in the list. The problem of determining for which values of n antipodal Gray codes can exist was posed by Hunter… (More)

A Venn diagram is simple if at most two curves intersect at any given point. A recent paper of Griggs, Killian, and Savage [Elec. J. Combinatorics, Research Paper 2, 2004] shows how to construct rotationally symmetric Venn diagrams for any prime number of curves. However, the resulting diagrams contain only n n/2 intersection points, whereas a simple Venn… (More)

Corrections This note contains corrections to two minor errors in [1]. First, the two figures that appear in Figure 10 [1, page 17] each have one of the quadrangulating edges misplaced: the relevant edge is drawn upwards from left-to-right whereas it should move be drawn upwards from right-to-left. The relevant edge occurs in the first quadrangulated region… (More)

In this paper we show that symmetric Venn diagrams for n sets exist for every prime n, settling an open question. Until this time, n = 11 was the largest prime for which the existence of such diagrams had been proven. We show that the problem can be reduced to finding a symmetric chain decomposition, satisfying a certain cover property, in a subposet of the… (More)

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