• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.437-445
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• 2003

We prove that H = (1, 3, 4, 5,...,6, 4, 3) is not alevel Artinian O-sequence.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.513-518
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• 2007

There is a one to one correspondence between Artinian algebras $k[x_1,...,x_n]/Ann(M)$ and finitely generated $k[x_1,...,x_n]-submodules$ M of $k[y_1,...,y_n]$ by Inverse System. In particular, any Artinian level algebra $k[x_1,...,x_n]/Ann(M)$ can be obtained when M is finitely generated by only maximal degree generators. We prove that H = (1, 4, 8, 13,..., 27, 8, 2) is not a level Artinian O-sequence using this inverse system.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.405-411
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• 2003

We prove that 25 different Artinian O-Sequences of codimension 3 type 3 with length 7 among all possible 334 cases are not level.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.605-614
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• 2005

We show that an Artinian O-sequence $h_0,h_1,{\cdots},h_{d-1},h_d\;=\;h_{d-1},h_{d+l}\;>\;h_d$ of codimension 3 is not level when $h_{d-1}\;=\;h_d\;=\;d + i\;and\;h{d+1}\;=\;d+(i+1)\;for\;i\;=\;1,\;2,\;and\;3$, which is a partial answer to the question in [9]. We also introduce an algorithm for finding noncancelable Betti numbers of minimal free resolutions of all possible Artinian O-sequences based on the theorem of Froberg and Laksov in [2].

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.433-440
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• 2003

Artinian O-sequences of codimension 3 and type 3 with length 7 are classified as level or non-level. Some cases are proved to be non-level among the 334 cases which have been suspected to be level.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.317-326
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• 2003

We classify all possible level Artinian O-sequences of socle degree 5 and type 3. Moreover, we show how to construct level Artinian algebras with those Hilbert functions using the sum of two ideals of finite sets of points in $P^2$ such that the ideal of the union of two sets is level.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.541-548
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• 2006

We find a graded Artinian level O-sequence of the form $H\;:\;h_0\;h_1\;\cdots\;h_{d-1}\;h_d\cdots$ $^{(d+1-1_)-st}h_d$ < $h_{d+s}$ not having the Weak-Lefschetz property. We also introduce several algorithms for construction of some examples of non-unimodal level O-sequences using a computer program called CoCoA.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.563-568
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• 2006

We introduce how to construct a non-unimodal level O-sequence which has all different local maxima as many as we desire.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.507-512
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• 2005

We find a condition that a graded Artinian O-sequence of codimension 4 is not level.