What is Left from The Lattics EO(7,8) when 1,..., 2i-3 are OCCUPIED but 2i-1 is free, for i=1..8

[Note that since 1,...,2i-3, are occupied, it follows that 2,...,2i-2 are unocuppied, and hence all vertices "above" them]

EO(7,8) itself

Here is the lattice EO(7,8) before anything is removed.

i=1

[Note that it is isomorphic to the Cartesian product of OE(7,7) (subtract 1 from all labels) . Of course P(-1) is empty.

i=2

[Note that it is isomorphic to the Cartesian product of OE(6,6) (subtract 3 from all labels) and the definutely occupied set {1} (in red). Of course P(0) is empty.

i=3

[Note that it is isomorphic to the Cartesian product of OE(5,5) (subtract 5 from all labels), P(1), and the definitely occupied set (in red) {1,3}.

i=4

[Note that it is isomorphic to the Cartesian product of OE(4,4) (subtract 7 from all labels), P(2), and the definitely occupied set (in red) {1,3,5}.

i=5

[Note that it is isomorphic to the Cartesian product of OE(3,3) (subtract 9 from all labels), P(3), and the definitely occupied set (in red) {1,3,5,7}.

i=6

[Note that it is isomorphic to the Cartesian product of OE(2,2) (subtract 11 from all labels), P(4), and the definitely occupied set (in red) {1,3,5,7,9}.

i=7

[Note that it is isomorphic to the Cartesian product of OE(1,1) (subtract 13 from all labels), P(5), and the definitely occupied set (in red) {1,3,5,7,9,11}.

i=8

[Note that it is isomorphic to the Cartesian product of OE(0,0) (of course it is empty), P(6), and the definitely occupied set (in red) {1,3,5,7,9,11,13}.

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