Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit expressions for the moments of the size of an (n, dn-1)-core
  partition with distinct parts   In a previous paper (arXiv:1608.02262), we used computer-assisted methods to
find explicit expressions for the moments of the size of a uniform random
(n,n+1)-core partition with distinct parts. In particular, we conjectured that
the distribution is asymptotically normal. However, our analysis hinged on a
characterization of (n,n+1)-core partitions given by Straub, which is not
readily generalized to other families of simultaneous core partitions.
  In another paper (arXiv:1611.05775) with Doron Zeilberger, we made use of the
characterization in terms of posets to analyze (2n+1,2n+3)-core partitions with
distinct parts; here, the distribution was found not to be asymptotically
normal. Our method involved finding recursive structure in the relevant
sequence of posets. We remarked that this method is applicable to other
families of core partitions, provided that one can understand the corresponding
posets.
  Here, we use the poset method (and, as before, a computer) to analyze
(n,dn-1)-core partitions with distinct parts, where d is a natural number.
(This problem was introduced by Straub in arXiv:1601.07161.) We exhibit
formulas for the moments of the size, as functions of d with n fixed, and vice
versa. We conjecture that the distribution is asymptotically normal as n
approaches infinity. Finally, we find formulas for the first few moments, as
functions of both n and d.

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The categories of this paper are: hep-th
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph