Monomial Ideals of Forest Type |
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| Authors: | Ali Soleyman Jahan Xinxian Zheng |
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| Institution: | 1. Department of Mathematics , University of Kurdistan , Sanadaj , Iranand School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iransolymanjahan@gmail.com;3. Fachbereich Mathematik und Informatik , Universit?t Duisburg–Essen , Essen , Germany |
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| Abstract: | As a generalization of the facet ideal of a forest, we define monomial ideal of forest type and show that monomial ideals of forest type are pretty clean. As a consequence, we show that if I is a monomial ideal of forest type in the polynomial ring S, then Stanley's decomposition conjecture holds for S/I. The other main result of this article shows that a clutter is totally balanced if and only if it has the free vertex property, and which is also equivalent to say that its edge ideal is a monomial ideal of forest type or is generated by an M sequence. |
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| Keywords: | Pretty clean modules Shellability Stanley decomposition |
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