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

Adriano Garsia, Gregg Musiker, Nolan Wallach, Guoce Xin

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 languageEnglish (US)
Pages (from-to)392-421
Number of pages30
JournalAdvances in Applied Mathematics
Issue number3
StatePublished - Mar 2009

Bibliographical note

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

Funding Information:
E-mail address: (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.


  • Diophantine system
  • Hilbert series
  • Invariant
  • Kronecker product


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