کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6425494 1633802 2016 59 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Local h-polynomials, invariants of subdivisions, and mixed Ehrhart theory
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Local h-polynomials, invariants of subdivisions, and mixed Ehrhart theory
چکیده انگلیسی

There are natural polynomial invariants of polytopes and lattice polytopes coming from enumerative combinatorics and Ehrhart theory, namely the h- and h⁎-polynomials, respectively. In this paper, we study their generalization to subdivisions and lattice subdivisions of polytopes. By abstracting constructions in mixed Hodge theory, we introduce multivariable polynomials which specialize to the h-, h⁎-polynomials. These polynomials, the mixed h-polynomial and the (refined) limit mixed h⁎-polynomial have rich symmetry, non-negativity, and unimodality properties, which both refine known properties of the classical polynomials, and reveal new structure. For example, we prove a lower bound theorem for a related invariant called the local h⁎-polynomial. We introduce our polynomials by developing a very general formalism for studying subdivisions of Eulerian posets that extends the work of Stanley, Brenti and Athanasiadis on local h-vectors. In particular, we prove a conjecture of Nill and Schepers, and answer a question of Athanasiadis.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 286, 2 January 2016, Pages 181-239
نویسندگان
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