Geodesic
Linear operators preserving column majorization of $(0, 1)$-vectors
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXVI, Tome 524 (2023), pp. 133-165

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The paper provides a characterization of linear operators preserving column majorization of $(0, 1)$-vectors. In addition, such operators are characterized explicitly in the case where they are given by special matrices, namely, $(\pm 1)$-matrices of order not exceeding $10$ or $(0, \pm 1)$-matrices of order not exceeding $5$. A number of related combinatorial-matrix-theory results are also proved. 
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     author = {P. M. Shteyner},
     title = {Linear operators preserving column majorization of $(0, 1)$-vectors},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {133--165},
     publisher = {mathdoc},
     volume = {524},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_524_a10/}
}
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P. M. Shteyner. Linear operators preserving column majorization of $(0, 1)$-vectors. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXVI, Tome 524 (2023), pp. 133-165. http://geodesic.mathdoc.fr/item/ZNSL_2023_524_a10/