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Congruence Properties of Andrews’SPT- Function

ABC Journal of Advanced Research

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Title Congruence Properties of Andrews’SPT- Function
Creator Das, Sabuj
Subject Crank, congruences, product notations, Ramanujan -type congruences, spt- function, vector partitions
Description Let spt (n) denote the total number of appearances of the smallest part in each partition of n. In 1988, Garvan gave new combinatorial interpretations of  Ramanujan’s partition congruences mod 5, 7 and 11 in terms of a crank for weighted vector partitions. This paper shows how to generate the generating functions for spt(n),  elaborately and also shows how to prove the relation among the terms spt (n) and. In 2008, Andrews stated Ramanujan- type congruences for the spt- function mod 5, 7 and 13. The new combinatorial  interpretations of the spt- congruences mod 5 and 7 are given in this article. These are in terms of the spt- crank but for a restricted set of vector partitions. The proofs depend on relating the spt- crank with the crank of vector partitions. 
Publisher i-Proclaim
Date 2014-12-30
Type info:eu-repo/semantics/article
Peer-reviewed Article
Format application/pdf
Source ABC Journal of Advanced Research; Vol 3, No 2 (2014): 6th Issue; 115-124
Language eng
Rights Copyright (c) 2016 Sabuj Das