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Dominance Orders, Generalized Binomial Coefficients, and Kummer’s Theorem

Tyler Ball, Tom Edgar and Daniel Juda
Mathematics Magazine
Vol. 87, No. 2 (April 2014), pp. 135-143
DOI: 10.4169/math.mag.87.2.135
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.87.2.135
Page Count: 9
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Dominance Orders, Generalized Binomial Coefficients, and Kummer’s Theorem
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Abstract

Summary We discuss the connections between a family of partial orders known as b-dominance orders, arithmetic in base b, and generalized binomial coefficients. In particular, we investigate theorems of Lucas and Kummer in relation to these orders and attempt to extend and explain these theorems using a family of generalized binomial coefficients derived from a simple integer sequence.

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