The asymptotic distribution of Andrews’ smallest parts function
نویسندگان
چکیده
منابع مشابه
A Combinatorial Proof of Andrews' Smallest Parts Partition Function
We give a combinatorial proof of Andrews' smallest parts partition function with the aid of rooted partitions introduced by Chen and the author.
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Let spt(n) denote the total number of appearances of smallest parts in the partitions of n. Recently, Andrews showed how spt(n) is related to the second rank moment, and proved some surprising Ramanujan-type congruences mod 5, 7 and 13. We prove a generalization of these congruences using known relations between rank and crank moments. We obtain an explicit Ramanujan-type congruence for spt(n) ...
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Recently, Andrews introduced the function s(n) = spt(n) which counts the number of smallest parts among the integer partitions of n. We show that its generating function satisfies an identity analogous to Ramanujan's mock theta identities. As a consequence, we are able to completely determine the parity of s(n). Using another type of identity, one based on Hecke operators, we obtain a complete ...
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We prove explicit congruences modulo powers of arbitrary primes for three smallest parts functions: one for partitions, one for overpartitions, and one for partitions without repeated odd parts. The proofs depend on `-adic properties of certain modular forms and mock modular forms of weight 3/2 with respect to the Hecke operators T (`).
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2015
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-015-0831-9