Geodesic
The realizability problem for values of the length function for quasi-commuting matrix pairs
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVIII, Tome 439 (2015), pp. 59-73

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The paper continues the investigation of the lengths of quasi-commuting matrix pairs; specifically, it considers the problem of realizability of different positive integers as values of the length function for quasi-commuting matrix pairs. 
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     author = {A. E. Guterman and O. V. Markova},
     title = {The realizability problem for values of the length function for quasi-commuting matrix pairs},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {59--73},
     publisher = {mathdoc},
     volume = {439},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_439_a5/}
}
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A. E. Guterman; O. V. Markova. The realizability problem for values of the length function for quasi-commuting matrix pairs. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVIII, Tome 439 (2015), pp. 59-73. http://geodesic.mathdoc.fr/item/ZNSL_2015_439_a5/