Name
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). |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.disc.2010.09.006 | Discrete Mathematics |
Keywords | Field | DocType |
determinant evaluations,monomial algebras,. weak lefschetz property. monomial algebras. complete intersections. character- istic p. plane partitions. determinant evaluations. 1,characteristic p,plane partitions,weak lefschetz property,complete intersections,plane partition,satisfiability,complete intersection | Discrete mathematics,Combinatorics,Algebraic number,Bijection,Prime number,Complete intersection,Characteristic function (probability theory),Monomial,Partition (number theory),Mathematics,Combinatorial commutative algebra | Journal |
Volume | Issue | ISSN |
310 | 24 | Discrete Mathematics |
Citations | PageRank | References |
0 | 0.34 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jizhou Li | 1 | 12 | 3.83 |
| Fabrizio Zanello | 2 | 15 | 4.46 |