On Divisibility of Some Sums of Binomial Coefficients Arising From Collection Formulas
Copyright policy )On Divisibility of Some Sums of Binomial Coefficients Arising From Collection Formulas
Summary: In this paper we establish a series of identities for sums of binomial coefficients to prove their divisibility by prime \(n\). These sums arise from exponents of commutators in collection formula for \((xy)^n\) with some restrictions on variables of the commutators.
- Siberian Federal University Russian Federation
собирательные формулы, делимость, Binomial coefficients; factorials; \(q\)-identities, divisibility, sums of binomial coefficients, суммы биномиальных коэффициентов, collection formulas, Factorials, binomial coefficients, combinatorial functions
собирательные формулы, делимость, Binomial coefficients; factorials; \(q\)-identities, divisibility, sums of binomial coefficients, суммы биномиальных коэффициентов, collection formulas, Factorials, binomial coefficients, combinatorial functions
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