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PROJ10.PRO
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1989-05-26
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PROJECT 10.
Consider the sequence of 2n x 2n anti-symmetric determinants:
│ 0 -1 │ │ 0 -1 -1 1 │ │ 0 -1 -1 -1 1 1 │
│ 1 0 │ , │ 1 0 -1 -1 │ , │ 1 0 -1 -1 -1 1 │ , ...
│ 1 1 0 -1 │ │ 1 1 0 -1 -1 -1 │
│ -1 1 1 0 │ │ 1 1 1 0 -1 -1 │
│ -1 1 1 1 0 -1 │
│ -1 -1 1 1 1 0 │
in which each entry in the first n subdiagonals below the main diagonal is 1 and each of the remaining entries below the main diagonal is -1.
Make a conjecture about the numerical values of determinants of this kind and try to prove it.