A Survey on Stanley Depth

  • Jürgen HerzogEmail author
Part of the Lecture Notes in Mathematics book series (LNM, volume 2083)


At the MONICA conference “MONomial Ideals, Computations and Applications” at the CIEM, Castro Urdiales (Cantabria, Spain) in July 2011, I gave three lectures covering different topics of Combinatorial Commutative Algebra: (1) A survey on Stanley decompositions. (2) Generalized Hibi rings and Hibi ideals. (3) Ideals generated by two-minors with applications to Algebraic Statistics. In this article I will restrict myself to give an extended presentation of the first lecture. The CoCoA tutorials following this survey will deal also with topics related to the other two lectures. Complementing the tutorials, the reader finds in [165] a CoCoA routine to compute the Stanley depth for modules of the form IJ, where JI are monomial ideals.


Prime Ideal Simplicial Complex Monomial Ideal Clean Module Prime Filtration 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Universität Duisburg-Essen Fachbereich MathematikEssenGermany

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