Notes on the spt function of George E . Andrews
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چکیده
Andrews defined spt(n) to be the total number of appearances of the smallest parts in all of the partitions of n. In this paper, we study the statistical distribution of spt(π), the number of smallest parts in the partition π as π ranges over all partitions of n. We also give a combinatorial proof of a conjecture of Hirschhorn, namely that p(0) + · · · + p(n− 1) < spt(n) < p(0) + · · · + p(n) for all n > 1, where p(n) is the number of partitions of n. Dedicated to George E. Andrews on the occasion of his 75th Birthday
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تاریخ انتشار 2013