DC Field | Value | Language |
dc.contributor.author | Bruns, Winfried | |
dc.contributor.author | Krattenthaler, Christian | |
dc.contributor.author | Uliczka, Jan | |
dc.date.accessioned | 2021-12-23T16:08:51Z | - |
dc.date.available | 2021-12-23T16:08:51Z | - |
dc.date.issued | 2010 | |
dc.identifier.issn | 19390807 | |
dc.identifier.uri | https://osnascholar.ub.uni-osnabrueck.de/handle/unios/8483 | - |
dc.description.abstract | Stanley decompositions of multigraded modules M over polynomial rings have been discussed intensively in recent years. There is a natural notion of depth that goes with a Stanley decomposition, called the Stanley depth. Stanley conjectured that the Stanley depth of a module M is always at least the (classical) depth of M. In this paper we introduce a weaker type of decomposition, which we call Hilbert decomposition, since it only depends on the Hilbert function of M, and an analogous notion of depth, called Hilbert depth. Since Stanley decompositions are Hilbert decompositions, the latter set upper bounds to the existence of Stanley decompositions. The advantage of Hilbert decompositions is that they are easier to find. We test our new notion on the syzygy modules of the residue class field of K [X-1, ... , X-n] (as usual identified with K). Writing M (n, k) for the k-th syzygy module, we show that the Hilbert depth of M (n, 1) is left perpendicular(n 1)/2right perpendicular. Furthermore, we show that, for n > k >= left perpendicular n/2right perpendicular, the Hilbert depth of M (n, k) is equal to n - 1. We conjecture that the same holds for the Stanley depth. For the range n/2 > k > 1, it seems impossible to come up with a compact formula for the Hilbert depth. Instead, we provide very precise asymptotic results as n becomes large. | |
dc.description.sponsorship | Austrian Science Foundation FWFAustrian Science Fund (FWF) [Z130-N13, S9607-N13]; Austrian Science Fund (FWF)Austrian Science Fund (FWF) [Z 130] Funding Source: researchfish; Research partially supported by the Austrian Science Foundation FWF, grants Z130-N13 and S9607-N13, the latter in the framework of the National Research Network ``Analytic Combinatorics and Probabilistic Number Theory.' | |
dc.language.iso | en | |
dc.publisher | ROCKY MT MATH CONSORTIUM | |
dc.relation.ispartof | JOURNAL OF COMMUTATIVE ALGEBRA | |
dc.subject | Mathematics | |
dc.title | STANLEY DECOMPOSITIONS AND HILBERT DEPTH IN THE KOSZUL COMPLEX | |
dc.type | journal article | |
dc.identifier.doi | 10.1216/JCA-2010-2-3-327 | |
dc.identifier.isi | ISI:000208459300004 | |
dc.description.volume | 2 | |
dc.description.issue | 3 | |
dc.description.startpage | 327 | |
dc.description.endpage | 357 | |
dc.identifier.eissn | 19392346 | |
dc.publisher.place | ARIZ STATE UNIV, DEPT MATH, TEMPE, AZ 85287-1904 USA | |
dcterms.isPartOf.abbreviation | J. Commut. Algebr. | |
dcterms.oaStatus | Green Submitted, hybrid | |
crisitem.author.dept | FB 06 - Mathematik/Informatik | - |
crisitem.author.deptid | fb06 | - |
crisitem.author.parentorg | Universität Osnabrück | - |
crisitem.author.netid | BrWi827 | - |