Monomial complete intersections, the weak Lefschetz property and plane partitions
Document Type
Article
Publication Date
12-28-2010
Abstract
We characterize the monomial complete intersections in three variables satisfying the Weak Lefschetz Property (WLP), as a function of the characteristic of the base field. Our result presents a surprising, and still combinatorially obscure, connection with the enumeration of plane partitions. It turns out that the rational primes p dividing the number, M(a,b,c), of plane partitions contained inside an arbitrary box of given sides a,b,c are precisely those for which a suitable monomial complete intersection (explicitly constructed as a bijective function of a,b,c) fails to have the WLP in characteristic p. We wonder how powerful can be this connection between combinatorial commutative algebra and partition theory. We present a first result in this direction, by deducing, using our algebraic techniques for the WLP, some explicit information on the rational primes dividing M(a,b,c). © 2010 Elsevier B.V. All rights reserved.
Publication Title
Discrete Mathematics
Recommended Citation
Li, J.,
&
Zanello, F.
(2010).
Monomial complete intersections, the weak Lefschetz property and plane partitions.
Discrete Mathematics,
310(24), 3558-3570.
http://doi.org/10.1016/j.disc.2010.09.006
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/6286