Geodesic
On the algebra generated by three commuting matrices: combinatorial cases
Matthew Satriano1 ; Ron Cherny1 ; Yohan Song1
1University of Waterloo
The electronic journal of combinatorics, Tome 31 (2024) no. 4
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Gerstenhaber proved in 1961 that the unital algebra generated by a pair of commuting $d \times d$ matrices over a field has dimension at most $d$. It is an open problem whether the analogous statement is true for triples of matrices which pairwise commute. We answer this question for special classes of triples of matrices arising from combinatorial data.
DOI : 10.37236/12909
Classification : 05E40, 15A27, 15A30, 15A21, 13E15, 15A45, 05B20
Mots-clés : Gerstenhaber problem, generating vectors

Matthew Satriano  1   ; Ron Cherny  1   ; Yohan Song  1

1 University of Waterloo 
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Matthew Satriano; Ron Cherny; Yohan Song. On the algebra generated by three commuting matrices: combinatorial cases. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12909

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