The Theorems of Oscillation of Sturm
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چکیده
complementary with respect to n of the given combination. Suppose now we form the nm combinations of any n numbers m at a time and consider the set of combinations formed by combining each of these nm combinations with their complementaries in such a way that the numbers in any combination arranged in their natural order are immediately followed by the numbers in the complementary combination arranged in the same way. The paper then gives an expression for the number of inversions in any combination of this set and also the excess of the number of combinations in the set which have an even number of inversions over those which have an odd number.
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تاریخ انتشار 2007