Sequence A025591 and MathSciNet

[Edwin Clark]

On Fri, 12 Dec 2003, Yuval Dekel wrote:

> If my memory is not mistaken, sequence A025591 is related to the following
> paper :
>
> Robert A. Proctor
> Solution of two difficult combinatorial problems with linear algebra,
> American Mathematical Monthly 89, 721-734.
>
> Perhaps someone on the list with an access to MathSciNet can share with us
> the abstract of this paper .

Here's the abstract. I don't see the connection.

MR0683197 (84f:05002)
Proctor, Robert A.
Solution of two difficult combinatorial problems with linear algebra.
Amer. Math. Monthly 89 (1982), no. 10, 721--734.
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The "subset sum problem" is the problem of finding a set of $n$ distinct
positive real numbers with as large a collection as possible of subsets
with the same sum. The "grid shading problem" is the problem of proving
the unimodality of the sequence $a_1,a_2,\cdots,a_{mn}$, where for fixed
$m$ and $n,a_i$ is the number of partitions of $i$ with at most $m$ parts
and largest part at most $n$. The grid shading problem was solved by J. J.
Sylvester [Philos. Mag. 5 (1878), 178--188; Jbuch 10, 82] using invariant
theory. The subset sum problem was solved by R. P. Stanley [SIAM J.
Algebraic Discrete Math. 1 (1980), 168--184; MR 82j:20083] using the tools
of algebraic geometry. (The answer is $\{1,2,\cdots,n\}$.)
This expository article contains the first elementary proofs of these
results. Only basic linear algebra is used, although the motivation for
the proof comes from the theory of representations of the Lie algebra
$\germ{sl}(2, C)$. The problems are restated in terms of certain posets,
which are shown to be rank unimodal and Sperner with the help of linear
operators on the vector spaces spanned by the pos