Appendix to the paper
Bozóki, S., Gál, P., Marosi, I., Weakley, W.D. (2019): Domination of the rectangular queen's graph, The Electronic Journal of Combinatorics 26(4) #P4.45

Sets of 8 queens that independently dominate the 14×14 chessboard


There are 55 different solutions; this file contains 55 of them.
Number of Orthodox Cover solutions is: 8.
Number of Centrally strong sets is: 0.
Number of expandable sets is: 0.

A dominating set is expandable if it covers a larger board than the one given.

Legend:
Sym (H) denotes reflection symmetry across the horizontal bisector.
Sym (V) denotes reflection symmetry across the vertical bisector.
Sym (C) denotes central symmetry about the center of the board.
Sym (D+) denotes reflection symmetry across the diagonal from lower left corner of the board.
Sym (D-) denotes reflection symmetry across the diagonal from top left corner of the board.
Sym (90) denotes 90 degree rotational symmetry about the center of the board.
The Sym (.) strings are printed without space next to the tables to help searching the solutions.

Δ denotes the absolute value of the difference of the number of queens on dark squares and of the ones on light squares.


14
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1
1234567891011121314

Solution #1

Δ=0
No symmetries

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1
1234567891011121314

Solution #2

Δ=0
No symmetries

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1
1234567891011121314

Solution #3

Δ=0
No symmetries

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1
1234567891011121314

Solution #4

Δ=0
No symmetries

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1
1234567891011121314

Solution #5

Δ=0
No symmetries

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1
1234567891011121314

Solution #6

Δ=0
No symmetries

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1
1234567891011121314

Solution #7

Δ=0
No symmetries

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1234567891011121314

Solution #8

Δ=0
No symmetries

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1234567891011121314

Solution #9

Δ=0
No symmetries

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1234567891011121314

Solution #10

Δ=0
No symmetries

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1234567891011121314

Solution #11

Δ=0
No symmetries

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1234567891011121314

Solution #12

Δ=0
No symmetries

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1
1234567891011121314

Solution #13

Δ=0
No symmetries

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Solution #14

Δ=0
No symmetries

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Solution #15

Δ=0
No symmetries

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1234567891011121314

Solution #16

Δ=0
No symmetries

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1234567891011121314

Solution #17

Δ=0
No symmetries

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1234567891011121314

Solution #18

Δ=0
No symmetries

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1234567891011121314

Solution #19

Δ=0
No symmetries

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1234567891011121314

Solution #20

Δ=0
No symmetries

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1234567891011121314

Solution #21

Δ=0
No symmetries

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1234567891011121314

Solution #22

Δ=0
No symmetries

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1234567891011121314

Solution #23

Δ=0
No symmetries

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1234567891011121314

Solution #24

Δ=0
No symmetries

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1234567891011121314

Solution #25

Δ=8
No symmetries
Orthodox cover

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1234567891011121314

Solution #26

Δ=8
No symmetries
Orthodox cover

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1234567891011121314

Solution #27

Δ=8
No symmetries
Orthodox cover

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1234567891011121314

Solution #28

Δ=8
No symmetries
Orthodox cover

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1234567891011121314

Solution #29

Δ=8
No symmetries
Orthodox cover

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1234567891011121314

Solution #30

Δ=8
No symmetries
Orthodox cover

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1234567891011121314

Solution #31

Δ=0
No symmetries

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1234567891011121314

Solution #32

Δ=0
No symmetries

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1234567891011121314

Solution #33

Δ=0
No symmetries

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1234567891011121314

Solution #34

Δ=0
No symmetries

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1234567891011121314

Solution #35

Δ=0
No symmetries

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1234567891011121314

Solution #36

Δ=0
No symmetries

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1234567891011121314

Solution #37

Δ=0
No symmetries

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1234567891011121314

Solution #38

Δ=0
No symmetries

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1234567891011121314

Solution #39

Δ=0
No symmetries

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1234567891011121314

Solution #40

Δ=0
No symmetries

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1234567891011121314

Solution #41

Δ=0
No symmetries

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1234567891011121314

Solution #42

Δ=0
No symmetries

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1234567891011121314

Solution #43

Δ=0
No symmetries

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1234567891011121314

Solution #44

Δ=0
Symmetries: Sym(C)

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1234567891011121314

Solution #45

Δ=0
No symmetries

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1234567891011121314

Solution #46

Δ=0
No symmetries

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1234567891011121314

Solution #47

Δ=0
No symmetries

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1234567891011121314

Solution #48

Δ=0
No symmetries

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1234567891011121314

Solution #49

Δ=0
No symmetries

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1234567891011121314

Solution #50

Δ=0
No symmetries

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1234567891011121314

Solution #51

Δ=0
No symmetries

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1234567891011121314

Solution #52

Δ=8
No symmetries
Orthodox cover

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1234567891011121314

Solution #53

Δ=8
No symmetries
Orthodox cover

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1234567891011121314

Solution #54

Δ=0
No symmetries

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1234567891011121314

Solution #55

Δ=0
No symmetries