An Alexander-Type duality for valuations

Karim A. Adiprasito; Raman Sanyal

doi:https://doi.org/10.1090/S0002-9939-2014-12366-5

An Alexander-Type duality for valuations

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Abstract

We prove an Alexander-type duality for valuations for certain subcomplexes in the boundary of polyhedra. These strengthen and simplify results of Stanley (1974) and Miller–Reiner (2005). We give a generalization of Brion’s theorem for this relative situation, and we discuss the topology of the possible subcomplexes for which the duality relation holds.

Original language	English
Pages (from-to)	833-843
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-2014-12366-5
State	Published - 2015
Externally published	Yes

All Science Journal Classification (ASJC) codes

Applied Mathematics
General Mathematics

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https://doi.org/10.1090/S0002-9939-2014-12366-5

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title = "An Alexander-Type duality for valuations",

abstract = "We prove an Alexander-type duality for valuations for certain subcomplexes in the boundary of polyhedra. These strengthen and simplify results of Stanley (1974) and Miller–Reiner (2005). We give a generalization of Brion{\textquoteright}s theorem for this relative situation, and we discuss the topology of the possible subcomplexes for which the duality relation holds.",

author = "Adiprasito, {Karim A.} and Raman Sanyal",

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T1 - An Alexander-Type duality for valuations

AU - Adiprasito, Karim A.

AU - Sanyal, Raman

PY - 2015

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N2 - We prove an Alexander-type duality for valuations for certain subcomplexes in the boundary of polyhedra. These strengthen and simplify results of Stanley (1974) and Miller–Reiner (2005). We give a generalization of Brion’s theorem for this relative situation, and we discuss the topology of the possible subcomplexes for which the duality relation holds.

AB - We prove an Alexander-type duality for valuations for certain subcomplexes in the boundary of polyhedra. These strengthen and simplify results of Stanley (1974) and Miller–Reiner (2005). We give a generalization of Brion’s theorem for this relative situation, and we discuss the topology of the possible subcomplexes for which the duality relation holds.

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U2 - https://doi.org/10.1090/S0002-9939-2014-12366-5

DO - https://doi.org/10.1090/S0002-9939-2014-12366-5

M3 - مقالة

SN - 0002-9939

VL - 143

SP - 833

EP - 843

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2

ER -

An Alexander-Type duality for valuations

Abstract

All Science Journal Classification (ASJC) codes

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