Invariants, Kronecker products, and combinatorics of some remarkable Diophantine systems

Adriano Garsia; Gregg Musiker; Nolan Wallach; Guoce Xin

doi:10.1016/j.aam.2008.09.002

Invariants, Kronecker products, and combinatorics of some remarkable Diophantine systems

Adriano Garsia, Gregg Musiker, Nolan Wallach, Guoce Xin

Mathematics

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6 Scopus citations

Abstract

This work lies across three areas (in the title) of investigation that are by themselves of independent interest. A problem that arose in quantum computing led us to a link that tied these areas together. This link consists of a single formal power series with a multifaced interpretation. The deeper exploration of this link yielded results as well as methods for solving some numerical problems in each of these separate areas.

Original language	English (US)
Pages (from-to)	392-421
Number of pages	30
Journal	Advances in Applied Mathematics
Volume	42
Issue number	3
DOIs	https://doi.org/10.1016/j.aam.2008.09.002
State	Published - Mar 2009

Bibliographical note

Funding Information:
Project of the Ministry of Education, the Ministry

Funding Information:
E-mail address: guoce.xin@gmail.com (G. Xin). 1 The fourth named author was supported by the 973 Project, the PCSIRT of Science and Technology, and the National Science Foundation of China.

Keywords

Diophantine system
Hilbert series
Invariant
Kronecker product

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title = "Invariants, Kronecker products, and combinatorics of some remarkable Diophantine systems",

abstract = "This work lies across three areas (in the title) of investigation that are by themselves of independent interest. A problem that arose in quantum computing led us to a link that tied these areas together. This link consists of a single formal power series with a multifaced interpretation. The deeper exploration of this link yielded results as well as methods for solving some numerical problems in each of these separate areas.",

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AU - Musiker, Gregg

AU - Wallach, Nolan

AU - Xin, Guoce

N1 - Funding Information: Project of the Ministry of Education, the Ministry Funding Information: E-mail address: guoce.xin@gmail.com (G. Xin). 1 The fourth named author was supported by the 973 Project, the PCSIRT of Science and Technology, and the National Science Foundation of China.

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N2 - This work lies across three areas (in the title) of investigation that are by themselves of independent interest. A problem that arose in quantum computing led us to a link that tied these areas together. This link consists of a single formal power series with a multifaced interpretation. The deeper exploration of this link yielded results as well as methods for solving some numerical problems in each of these separate areas.

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KW - Hilbert series

KW - Invariant

KW - Kronecker product

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Invariants, Kronecker products, and combinatorics of some remarkable Diophantine systems

Abstract

Bibliographical note

Keywords

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