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

School of Mathematics

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

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: [email protected] (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

Publisher link

10.1016/j.aam.2008.09.002

Find It

Find It at U of M Libraries

Cite this

@article{a7ae71206b2644e2aa52f835b4653292,

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.",

keywords = "Diophantine system, Hilbert series, Invariant, Kronecker product",

author = "Adriano Garsia and Gregg Musiker and Nolan Wallach and Guoce Xin",

note = "Funding Information: Project of the Ministry of Education, the Ministry Funding Information: E-mail address: [email protected] (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.",

year = "2009",

month = mar,

doi = "10.1016/j.aam.2008.09.002",

language = "English (US)",

volume = "42",

pages = "392--421",

journal = "Advances in Applied Mathematics",

issn = "0196-8858",

publisher = "Academic Press Inc.",

number = "3",

}

TY - JOUR

T1 - Invariants, Kronecker products, and combinatorics of some remarkable Diophantine systems

AU - Garsia, Adriano

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: [email protected] (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.

PY - 2009/3

Y1 - 2009/3

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.

AB - 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.

KW - Diophantine system

KW - Hilbert series

KW - Invariant

KW - Kronecker product

UR - http://www.scopus.com/inward/record.url?scp=61349189543&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=61349189543&partnerID=8YFLogxK

U2 - 10.1016/j.aam.2008.09.002

DO - 10.1016/j.aam.2008.09.002

M3 - Article

AN - SCOPUS:61349189543

SN - 0196-8858

VL - 42

SP - 392

EP - 421

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

IS - 3

ER -

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

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this