Geodesic
Description of pairs of anti-commuting Toeplitz and Hankel matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXX, Tome 463 (2017), pp. 160-223

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A complete description of the sets of pairs of anti-commuting Toeplitz and Hankel matrices is given. 
@article{ZNSL_2017_463_a12,
     author = {Kh. D. Ikramov and V. N. Chugunov},
     title = {Description of pairs of anti-commuting {Toeplitz} and  {Hankel} matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {160--223},
     publisher = {mathdoc},
     volume = {463},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_463_a12/}
}
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Kh. D. Ikramov; V. N. Chugunov. Description of pairs of anti-commuting Toeplitz and  Hankel matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXX, Tome 463 (2017), pp. 160-223. http://geodesic.mathdoc.fr/item/ZNSL_2017_463_a12/