Abstract
A partition of a positive integer \(n\) is a non-increasing sequence of positive integers whose sum is \(n\). It may be represented by a Ferrers diagram. These diagrams contain corners which are points of degree two. We define corners of types \((a,b)\), \((a+,b)\) and \((a+,b+)\), and also define the size of a corner. Via a generating function, we count corners of each type and corners of size \(m\). We also find asymptotics for the number of corners as \(n\) tends to infinity.
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Charlotte Brennan and Arnold Knopfmacher were supported by the National Research Foundation under Grant Numbers 86329 and 81021, respectively.
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Blecher, A., Brennan, C., Knopfmacher, A. et al. Counting corners in partitions. Ramanujan J 39, 201–224 (2016). https://doi.org/10.1007/s11139-014-9666-4
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DOI: https://doi.org/10.1007/s11139-014-9666-4