Inequalities for cd-indices of joins and products of polytopes

Richard Ehrenborg; Harold Fox.

doi:10.1007/s00493-003-0026-z

Inequalities for cd-indices of joins and products of polytopes

Richard Ehrenborg, Harold Fox.

Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

The cd-index is a polynomial which encodes the flag f-vector of a convex polytope. For polytopes U and V, we determine explicit recurrences for computing the cd-index of the free join U circle inside V sign V and the cd-index of the Cartesian product U × V. As an application of these recurrences, we prove the inequality Ψ(U circle inside V sign (V circle inside V sign W)) ≤ Ψ((U circle inside V sign V) × W) involving the cd-indices of three polytopes.

Original language	English
Pages (from-to)	427-452
Number of pages	26
Journal	Combinatorica
Volume	23
Issue number	3
DOIs	https://doi.org/10.1007/s00493-003-0026-z
State	Published - 2003

Bibliographical note

Funding Information:
We thank Louis Bil l era, Margaret Readdy and the two referees for their generous comments. This research was partial l y supported by National Science Foundation DMS 96-19681 as part of an REU project at Cornel l University. The first author was also partially supported by National Science Foundation, DMS 97-29992, and NEC Research Institute, Inc.

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1007/s00493-003-0026-z

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title = "Inequalities for cd-indices of joins and products of polytopes",

abstract = "The cd-index is a polynomial which encodes the flag f-vector of a convex polytope. For polytopes U and V, we determine explicit recurrences for computing the cd-index of the free join U circle inside V sign V and the cd-index of the Cartesian product U × V. As an application of these recurrences, we prove the inequality Ψ(U circle inside V sign (V circle inside V sign W)) ≤ Ψ((U circle inside V sign V) × W) involving the cd-indices of three polytopes.",

author = "Richard Ehrenborg and Harold Fox.",

note = "Funding Information: We thank Louis Bil l era, Margaret Readdy and the two referees for their generous comments. This research was partial l y supported by National Science Foundation DMS 96-19681 as part of an REU project at Cornel l University. The first author was also partially supported by National Science Foundation, DMS 97-29992, and NEC Research Institute, Inc.",

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T1 - Inequalities for cd-indices of joins and products of polytopes

AU - Ehrenborg, Richard

AU - Fox., Harold

N1 - Funding Information: We thank Louis Bil l era, Margaret Readdy and the two referees for their generous comments. This research was partial l y supported by National Science Foundation DMS 96-19681 as part of an REU project at Cornel l University. The first author was also partially supported by National Science Foundation, DMS 97-29992, and NEC Research Institute, Inc.

PY - 2003

Y1 - 2003

N2 - The cd-index is a polynomial which encodes the flag f-vector of a convex polytope. For polytopes U and V, we determine explicit recurrences for computing the cd-index of the free join U circle inside V sign V and the cd-index of the Cartesian product U × V. As an application of these recurrences, we prove the inequality Ψ(U circle inside V sign (V circle inside V sign W)) ≤ Ψ((U circle inside V sign V) × W) involving the cd-indices of three polytopes.

AB - The cd-index is a polynomial which encodes the flag f-vector of a convex polytope. For polytopes U and V, we determine explicit recurrences for computing the cd-index of the free join U circle inside V sign V and the cd-index of the Cartesian product U × V. As an application of these recurrences, we prove the inequality Ψ(U circle inside V sign (V circle inside V sign W)) ≤ Ψ((U circle inside V sign V) × W) involving the cd-indices of three polytopes.

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DO - 10.1007/s00493-003-0026-z

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JO - Combinatorica

JF - Combinatorica

IS - 3

ER -

Inequalities for cd-indices of joins and products of polytopes

Abstract

Bibliographical note

ASJC Scopus subject areas

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