On Stanley Depths of Certain Monomial Factor Algebras
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Bibliographic record
Abstract
Abstract Let S = K[x 1 , . . . , x n ] be the polynomial ring in n-variables over a ûeld K and I a monomial ideal of S. According to one standard primary decomposition of I, we get a Stanley decomposition of the monomial factor algebra S/I. Using this Stanley decomposition, one can estimate the Stanley depth of S/I. It is proved that sdepth S (S/I) ≤ size S (I). When I is squarefree and bigsize S (I) ≤ 2, the Stanley conjecture holds for S/I, i.e., sdepth S (S/I) ≥ depthS(S/I).
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.009 | 0.005 |
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