Lower Bounds on the Graver Complexity of M-Fold Matrices

Elisabeth Finhold; Raymond Hemmecke

doi:10.1007/s00026-015-0297-2

Lower Bounds on the Graver Complexity of M-Fold Matrices

Elisabeth Finhold
, Raymond Hemmecke

Computation, Information and Technology

Technical University of Munich

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

7 Scopus citations

Abstract

In this paper, we present a construction that turns certain relations on Graver basis elements of an M-fold matrix (Formula presented.) into relations on Graver basis elements of an (Formula presented.) -fold matrix (Formula presented.). In doing so, we strengthen the bound on the Graver complexity of the M-fold matrix (Formula presented.) from (Formula presented.) (Berstein and Onn) to (Formula presented.) , for (Formula presented.). Moreover, we give a lower bound on the Graver complexity (Formula presented.) of general (Formula presented.) -fold matrices (Formula presented.) and we prove that the bound for (Formula presented.) is not tight.

Original language	English
Pages (from-to)	73-85
Number of pages	13
Journal	Annals of Combinatorics
Volume	20
Issue number	1
DOIs	https://doi.org/10.1007/s00026-015-0297-2
State	Published - 1 Mar 2016

Keywords

Graver basis
Graver complexity
lower bound

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10.1007/s00026-015-0297-2

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abstract = "In this paper, we present a construction that turns certain relations on Graver basis elements of an M-fold matrix (Formula presented.) into relations on Graver basis elements of an (Formula presented.) -fold matrix (Formula presented.). In doing so, we strengthen the bound on the Graver complexity of the M-fold matrix (Formula presented.) from (Formula presented.) (Berstein and Onn) to (Formula presented.) , for (Formula presented.). Moreover, we give a lower bound on the Graver complexity (Formula presented.) of general (Formula presented.) -fold matrices (Formula presented.) and we prove that the bound for (Formula presented.) is not tight.",

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AU - Hemmecke, Raymond

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N2 - In this paper, we present a construction that turns certain relations on Graver basis elements of an M-fold matrix (Formula presented.) into relations on Graver basis elements of an (Formula presented.) -fold matrix (Formula presented.). In doing so, we strengthen the bound on the Graver complexity of the M-fold matrix (Formula presented.) from (Formula presented.) (Berstein and Onn) to (Formula presented.) , for (Formula presented.). Moreover, we give a lower bound on the Graver complexity (Formula presented.) of general (Formula presented.) -fold matrices (Formula presented.) and we prove that the bound for (Formula presented.) is not tight.

AB - In this paper, we present a construction that turns certain relations on Graver basis elements of an M-fold matrix (Formula presented.) into relations on Graver basis elements of an (Formula presented.) -fold matrix (Formula presented.). In doing so, we strengthen the bound on the Graver complexity of the M-fold matrix (Formula presented.) from (Formula presented.) (Berstein and Onn) to (Formula presented.) , for (Formula presented.). Moreover, we give a lower bound on the Graver complexity (Formula presented.) of general (Formula presented.) -fold matrices (Formula presented.) and we prove that the bound for (Formula presented.) is not tight.

KW - Graver basis

KW - Graver complexity

KW - lower bound

UR - https://www.scopus.com/pages/publications/84958760923

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M3 - Article

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SN - 0218-0006

VL - 20

SP - 73

EP - 85

JO - Annals of Combinatorics

JF - Annals of Combinatorics

IS - 1

ER -

Lower Bounds on the Graver Complexity of M-Fold Matrices

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Keywords

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