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A Survey on Stanley Depth

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Monomial Ideals, Computations and Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2083))

Abstract

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 I ∕ J, where J ⊂ I are monomial ideals.

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Authors and Affiliations

  1. Universität Duisburg-Essen Fachbereich Mathematik, Campus Essen, 45117, Essen, Germany

    Jürgen Herzog

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  1. Jürgen Herzog
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Correspondence to Jürgen Herzog .

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Editors and Affiliations

  1. Universitá degli Studi di Genova Dipartimento di Matematica, Genova, Italy

    Anna M. Bigatti

  2. Geometría y Topología, University of Valladolid, Dpto. de Álgebra, Análisis Matemático, Valladolid, Spain

    Philippe Gimenez

  3. University of La Rioja Matemáticas y Computación, Logroño, Spain

    Eduardo Sáenz-de-Cabezón

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Herzog, J. (2013). A Survey on Stanley Depth. In: Bigatti, A., Gimenez, P., Sáenz-de-Cabezón, E. (eds) Monomial Ideals, Computations and Applications. Lecture Notes in Mathematics, vol 2083. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38742-5_1

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