Hyperdeterminants on meet-semilattices

Abstract

In this paper, we first present an explicit factorization expression of hyperdeterminants of Cohen even functions defined on cartesian powers of meet-semilattices, which is a unified generalization of results in previous literatures. Then applying this expression, we evaluate a kind of hyperdeterminants associated with coprime decomposable meet-semilattices. This gives a complete solution of a problem raised in [Hong S, Li M, and Wang B. Hyperdeterminants associated with multiple even functions, Ramanujan J. 2014;34:265–281].

Keywords:

• hyperdeterminant
• Cohen even function
• meet-semilattice
• coprime decomposable meet-semilattices

AMS Subject Classifications:

• Primary: 06A12
• 11C20
• 15A15
• 15A69
• 15B99

Acknowledgements

The authors would like to thank the anonymous referee for helpful comments.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

S. Hong was supported partially by National Science Foundation of China [grant number #11371260].