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Hook lengths and shifted parts of partitions

✍ Scribed by Guo-Niu Han

Publisher
Springer US
Year
2009
Tongue
English
Weight
296 KB
Volume
23
Category
Article
ISSN
1382-4090

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πŸ“œ SIMILAR VOLUMES

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We study the generating function for Q(n), the number of partitions of a natural number n into distinct parts. Using the arithmetic properties of Fourier coefficients of integer weight modular forms, we prove several theorems on the divisibility and distribution of Q(n) modulo primes p 5.

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For a graph G, let ' 2 (G ) denote the minimum degree sum of a pair of nonadjacent vertices. We conjecture that if |V(G)| n i 1 k a i and ' 2 (G ) ! n k Γ€ 1, then for any k vertices v 1 , v 2 , F F F , v k in G, there exist vertex-disjoint paths P 1 , P 2 , F F F , P k such that |V (P i )| a i and v