[問題] Combinatorics
Start with a row containing all positive integers. Then delete every mth
column. Then replace the remaining entries by partial sums. Delete every
(m-1)st column. Then replace with partial sums again, and so on. Show that
the final result is a sequence of mth powers.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 2 3 4 6 7 8 9 11 12 13 14
1 3 6 10 16 23 31 40 51 63 76 90
1 3 6 16 23 31 51 63 76
1 4 10 26 49 80 131 194 270
1 4 26 49 131 194
1 5 31 80 211 405
1 31 211
1 32 243
1^5 2^5 3^5
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