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Alexander duals of multipermutohedron ideals

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Abstract

An Alexander dual of a multipermutohedron ideal has many combinatorial properties. The standard monomials of an Artinian quotient of such a dual correspond bijectively to some λ-parking functions, and many interesting properties of these Artinian quotients are obtained by Postnikov and Shapiro (Trans. Am. Math. Soc. 356 (2004) 3109–3142). Using the multigraded Hilbert series of an Artinian quotient of an Alexander dual of multipermutohedron ideals, we obtained a simple proof of Steck determinant formula for enumeration of λ-parking functions. A combinatorial formula for all the multigraded Betti numbers of an Alexander dual of multipermutohedron ideals are also obtained.

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  1. Indian Institute of Science Education and Research Mohali, Knowledge City, Sector 81, SAS Nagar, 140 306, India

    Ajay Kumar & Chanchal Kumar

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  1. Ajay Kumar
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  2. Chanchal Kumar
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Correspondence to Chanchal Kumar.

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Kumar, A., Kumar, C. Alexander duals of multipermutohedron ideals. Proc Math Sci 124, 1–15 (2014). https://doi.org/10.1007/s12044-014-0164-9

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  • DOI: https://doi.org/10.1007/s12044-014-0164-9

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