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On the Distribution of the spt-Crank - Open Access Library
Source: oalib.com
Article summary:
1. Andrews, Garvan and Liang introduced the spt-crank for vector partitions.
2. The article conjectures that for any n the sequence {NS ( m, n) } m is unimodal, where NS ( m, n) is the number of S-partitions of size n with crank m weight by the spt-crank.
3. The article provides an asymptotic study for the distribution of the spt-crank statistic and speculates about a definition for the spt-crank in terms of “marked” partitions.
Article analysis:
The article is generally reliable and trustworthy in its presentation of information and claims. It provides evidence to support its conjecture that for any n the sequence {NS (m,n)} m is unimodal, where NS (m,n) is the number of S-partitions of size n with crank m weight by the spt-crank. Additionally, it provides an asymptotic study for the distribution of the spt-crank statistic and speculates about a definition for the spt-crank in terms of “marked” partitions.
The article does not appear to be biased or one sided in its reporting or presentation of information. It does not make unsupported claims or omit points of consideration or evidence needed to support its claims. It does not appear to be promotional in nature or partial towards any particular point of view or opinion on this topic. The article also notes possible risks associated with its conclusions and presents both sides equally when discussing potential interpretations and implications of its findings.