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@article{MZM_2012_92_5_a4, author = {A. \`E. Guterman and G. Dolinar and B. Kuzma}, title = {P\'olya {Convertibility} {Problem} for {Symmetric} {Matrices}}, journal = {Matemati\v{c}eskie zametki}, pages = {684--698}, publisher = {mathdoc}, volume = {92}, number = {5}, year = {2012}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_5_a4/} }
A. È. Guterman; G. Dolinar; B. Kuzma. P\'olya Convertibility Problem for Symmetric Matrices. Matematičeskie zametki, Tome 92 (2012) no. 5, pp. 684-698. http://geodesic.mathdoc.fr/item/MZM_2012_92_5_a4/
[1] G. Pólya, “Aufgabe 424”, Arch. Math. Phys., 20:3 (1913), 271
[2] G. Szegö, “Lösung zu 424”, Arch. Math. Phys., 21 (1913), 291–292
[3] P. Botta, “On the conversion of the determinant into the permanent”, Canad. Math. Bull., 11 (1968), 31–34 | DOI | MR | Zbl
[4] M. P. Coelho, M. A. Duffner, “Immanant preserving and immanant converting maps”, Linear Algebra Appl., 418:1 (2006), 177–187 | DOI | MR | Zbl
[5] M. Marcus, H. Minc, “On the relation between the determinant and the permanent”, Illinois J. Math., 5 (1961), 376–381 | MR | Zbl
[6] R. A. Brualdi, B. L. Shader, “On sign-nonsingular matrices and the conversion of the permanent into the determinant”, Applied Geometry and Discrete Mathematics, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 4, Amer. Math. Soc., Providence, RI, 1991, 117–134 | MR | Zbl
[7] G. Dolinar, A. Guterman, B. Kuzma, M. Orel, “On the Pólya permanent problem over finite fields”, European J. Combin., 32:1 (2011), 116–132 | DOI | MR | Zbl
[8] W. McCuaig, “Pólya's permanent problem”, Electron. J. Combin., 11 (2004), Research Paper 79 | MR | Zbl
[9] G. Kuperberg, “An exploration of the permanent-determinant method”, Electron. J. Combin., 5 (1998), Research Paper 46 | MR | Zbl
[10] P. W. Kasteleyn, “The statistics of dimers on a lattice. I. The number of dimer arrangements on a quadratic lattice”, Physica, 27:12 (1961), 1209–1225 | DOI | Zbl
[11] H. N. V. Temperley, M. E. Fisher, “Dimer problem in statistical mechanics – an exact result”, Philos. Mag., 6:68 (1961), 1061–1063 | DOI | MR | Zbl
[12] M. H. Lim, “A note on the relation between the determinant and the permanent”, Linear and Multilinear Algebra, 7:2 (1979), 145–147 | DOI | MR | Zbl
[13] M. P. Coelho, M. A. Duffner, “On the relation between the determinant and the permanent on symmetric matrices”, Linear and Multilinear Algebra, 51:2 (2003), 127–136 | DOI | MR | Zbl
[14] M. P. Coelho, M. A. Duffner, “On the conversion of an immanant into another on symmetric matrices”, Linear and Multilinear Algebra, 51:2 (2003), 137–145 | DOI | MR | Zbl
[15] M. P. Coelho, M. A. Duffner, “Subspaces where an immanant is convertible into its conjugate”, Linear and Multilinear Algebra, 48:4 (2001), 383–408 | DOI | MR | Zbl
[16] P. M. Gibson, “Conversion of the permanent into the determinant”, Proc. Amer. Math. Soc., 27 (1971), 471–476 | DOI | MR | Zbl
[17] C. H. C. Little, “A characterization of convertible $(0,1)$-matrices”, J. Combinatorial Theory Ser. B, 18:3 (1975), 187–208 | DOI | MR | Zbl
[18] G. Dolinar, A. E. Guterman, B. Kuzma, “Barery Gibsona dlya problemy Polia”, Fundament. i prikl. matem., 16:8 (2010), 73–86 | MR
[19] P. M. Gibson, “An identity between permanents and determinants”, Amer. Math. Monthly, 76:3 (1969), 270–271 | DOI | MR | Zbl
[20] H. Minc, Permanents, Encyclopedia Math. Appl., 6, Addison-Wesley Publ., Reading, MA, 1978 | MR | Zbl