Partitions into prime powers.
نویسندگان
چکیده
منابع مشابه
Partitions of an Integer into Powers
In this paper, we use a simple discrete dynamical model to study partitions of integers into powers of another integer. We extend and generalize some known results about their enumeration and counting, and we give new structural results. In particular, we show that the set of these partitions can be ordered in a natural way which gives the distributive lattice structure to this set. We also giv...
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Let p be any prime, and let α and n be nonnegative integers. Let r ∈ Z and f (x) ∈ Z[x]. We establish the congruence p deg f k≡r (mod p α) n k (−1) k f k − r p α ≡ 0 mod p ∞ i=α ⌊n/p i ⌋ (motivated by a conjecture arising from algebraic topology), and obtain the following vast generalization of Lucas' theorem: If α > 1 and l, s, t are nonnegative integers with s, t < p, then 1 ⌊n/p α−1 ⌋! k≡r (...
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Many textbooks contain material on partitions. Two standard references are [A] and [S]. A partition of a natural integer n with parts λ1, . . . , λk is a finite decreasing sequence λ = (λ1 ≥ λ2 ≥ · · · ≥ λk > 0) of natural integers λ1, . . . , λk > 0 such that n = ∑k i=1 λi. We denote by |λ| the content n of λ. Partitions are also written as sums: n = λ1 + · · ·+ λk and one uses also the (abusi...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1960
ISSN: 0026-2285
DOI: 10.1307/mmj/1028998381