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Questions tagged [planar-partitions]

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2
votes
0answers
58 views

8-partition of a planar convex body by 4 concurrent lines

It is known1 that any convex body $K$ in the plane can be partitioned into $6$ equal-area pieces by $3$ concurrent lines which meet at a point in $K$. Call this a $6$-partition. This result cannot be ...
12
votes
1answer
301 views

Counting higher-dimensional partitions with symmetric function theory

My coauthors and I are writing a (mostly expository) paper in which we construct the Specht module. Our proof that the Specht module is irreducible in characteristic zero implies the following ...
19
votes
0answers
297 views

“quantum” symmetric plane partitions beget alternating sign matrices?

The "quantum" version qTSPP of the number of totally symmetric plane partitions, contained in the cube $[0,n]^3$, is enumerated by $$f_n(q):=\prod_{j=1}^n\prod_{k=1}^j\prod_{\ell=1}^k\frac{1-q^{j+k+\...