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Dominance Orders, Generalized Binomial Coefficients, and Kummer’s Theorem
Tyler Ball, Tom Edgar and Daniel Juda
Vol. 87, No. 2 (April 2014), pp. 135-143
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.87.2.135
Page Count: 9
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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.
Copyright the Mathematical Association of America 2014