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O ct 1 99 8 Another combinatorial determinant
= 1!2! · · ·n!b n(n+1)/2 1 (n = 0, 1, 2, . . . ). In fact, we prove both of these theorems at once, by formulating and proving a common generalization. In both theorems, each row of the matrix is obtained from the previous row by applying a certain transformation of power series: in Theorem 1, the transformation is t 7→ t(1 + a1x + a2x 2 + · · · ), while in Theorem 2, the transformation is t 7→...
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= 1!2! · · ·n!b n(n+1)/2 1 (n = 0, 1, 2, . . . ). In fact, we prove both of these theorems at once, by formulating and proving a common generalization. In both theorems, each row of the matrix is obtained from the previous row by applying a certain transformation of power series: in Theorem 1, the transformation is t 7→ t(1 + a1x + a2x 2 + · · · ), while in Theorem 2, the transformation is t 7→...
متن کامل8 M ay 1 99 9 Another combinatorial determinant
= 1!2! · · ·n!b n(n+1)/2 1 (n = 0, 1, 2, . . . ). In fact, we prove both of these theorems at once, by formulating and proving a common generalization. In both theorems, each row of the matrix is obtained from the previous row by applying a certain transformation of power series: in Theorem 1, the transformation is t 7→ t(1 + a1x + a2x 2 + · · · ), while in Theorem 2, the transformation is t 7→...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2000
ISSN: 0097-3165
DOI: 10.1006/jcta.1999.3029