Glaeser Dominos

A puzzle by George Glaeser: fit the following 28 dominos: on the (7 x 8) matrix
00
01
02
03
04
05
06
11
12
13
14
15
16
 
22
23
24
25
26
   
   
33
34
35
36
   
   
   
44
45
46
   
   
   
   
55
56
   
   
   
   
   
66
   
   
   
   
   
   
3620044
6551523
6115063
2220010
2114355
4364422
4505334
1630166
Solution: Below is the solution. An exhaustive search shows that the matrix A can be covered in exactly one way by the 28 dominos (i,j), 0 < i <= j < 7. We call the 7x8 matrix a Glaeser matrix.
Question:


The Glaeser Puzzle shows that for n=7, there is a Glaeser Matrix. For n=2, there is no Glaeser Matrix: the 3 Glaeser dominos (0,0),(1,1),(0,1) can not be arranged uniquely on a 2 x 3 board. For n=3, there is a Glaeser matrix:


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