Two Remarks on Independent Sets |
| |
Authors: | Hans-Gert Gräbe |
| |
Institution: | (1) Universität Leipzig, Fachbereich Mathematik/Informatik, Augustusplatz 10-11, O - 7010 Leipzig, Germany |
| |
Abstract: | In the first part we generalize the notion of strongly independent sets, introduced in 10] for polynomial ideals, to submodules of free modules and explain their computational relevance. We discuss also two algorithms to compute strongly independent sets that rest on the primary decomposition of squarefree monomial ideals.Usually the initial ideal in(I) of a polynomial ideal I is worse than I. In 9] the authors observed that nevertheless in(I) is not as bad as one should expect, showing that in(I) is connected in codimension one if I is prime.In the second part of the paper we add more evidence to that observation. We show that in(I) inherits (radically) unmixedness, connectedness in codimension one and connectedness outside a finite set of points from I and prove the same results also for initial submodules of free modules. The proofs use a deformation from I to in(I ). |
| |
Keywords: | independent set initial ideal unmixedness connectedness in codimension |
本文献已被 SpringerLink 等数据库收录! |
|