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acute simplex; nonobtuse simplex; orthogonal simplex; $0/1$-matrix; doubly stochastic matrix; fully indecomposable matrix; partly decomposable matrix

References:

[1] Bapat, R. B., Raghavan, T. E. S.: **Nonnegative Matrices and Applications**. Encyclopedia of Mathematics and Applications 64, Cambridge University Press, Cambridge (1997). DOI 10.1017/CBO9780511529979 | MR 1449393 | Zbl 0879.15015

[2] Berman, A., Plemmons, R. J.: **Nonnegative Matrices in the Mathematical Sciences**. Classics in Applied Mathematics 9, SIAM, Philadelphia (1994). DOI 10.1137/1.9781611971262 | MR 1298430 | Zbl 0815.15016

[3] Braess, D.: **Finite Elements. Theory, Fast Solvers, and Applications in Solid Mechanics**. Cambridge University Press, Cambridge (2001). DOI 10.1017/CBO9780511618635 | MR 1827293 | Zbl 0976.65099

[4] Brandts, J., Cihangir, A.: **Counting triangles that share their vertices with the unit $n$-cube**. Proc. Conf. Applications of Mathematics 2013 J. Brandts et al. Institute of Mathematics AS CR, Praha (2013), 1-12. MR 3204425 | Zbl 1340.52020

[5] Brandts, J., Cihangir, A.: **Geometric aspects of the symmetric inverse M-matrix problem**. Linear Algebra Appl. 506 (2016), 33-81. DOI 10.1016/j.laa.2016.05.015 | MR 3530670 | Zbl 1382.15047

[6] Brandts, J., Cihangir, A.: **Enumeration and investigation of acute $0/1$-simplices modulo the action of the hyperoctahedral group**. Spec. Matrices 5 (2017), 158-201. DOI 10.1515/spma-2017-0014 | MR 3707128 | Zbl 1392.05019

[7] Brandts, J., Dijkhuis, S., Haan, V. de, Křížek, M.: **There are only two nonobtuse triangulations of the unit $n$-cube**. Comput. Geom. 46 (2013), 286-297. DOI 10.1016/j.comgeo.2012.09.005 | MR 2994435 | Zbl 1261.65020

[8] Brandts, J., Korotov, S., Křížek, M.: **Dissection of the path-simplex in $\mathbb{R}^n$ into $n$ path-subsimplices**. Linear Algebra Appl. 421 (2007), 382-393. DOI 10.1016/j.laa.2006.10.010 | MR 2294350 | Zbl 1112.51006

[9] Brandts, J., Korotov, S., Křížek, M.: **The discrete maximum principle for linear simplicial finite element approximations of a reaction-diffusion problem**. Linear Algebra Appl. 429 (2008), 2344-2357. DOI 10.1016/j.laa.2008.06.011 | MR 2456782 | Zbl 1154.65086

[10] Brandts, J., Korotov, S., Křížek, M., Šolc, J.: **On nonobtuse simplicial partitions**. SIAM Rev. 51 (2009), 317-335. DOI 10.1137/060669073 | MR 2505583 | Zbl 1172.51012

[11] Brenner, S. C., Scott, L. R.: **The Mathematical Theory of Finite Element Methods**. Texts in Applied Mathematics 15, Spinger, New York (1994). DOI 10.1007/978-1-4757-4338-8 | MR 1278258 | Zbl 0804.65101

[12] Brualdi, R. A.: **Combinatorial Matrix Classes**. Encyclopedia of Mathematics and Its Applications 108, Cambridge University Press, Cambridge (2006). DOI 10.1017/CBO9780511721182 | MR 2266203 | Zbl 1106.05001

[13] Brualdi, R. A., Ryser, H. J.: **Combinatorial Matrix Theory**. Encyclopedia of Mathematics and Its Applications 39, Cambridge University Press, Cambridge (1991). DOI 10.1017/CBO9781107325708 | MR 1130611 | Zbl 0746.05002

[14] Fiedler, M.: **Über qualitative Winkeleigenschaften der Simplexe**. Czech. Math. J. 7 (1957), 463-478 German. MR 0094740 | Zbl 0093.33602

[15] Grigor'ev, N. A.: **Regular simplices inscribed in a cube and Hadamard matrices**. Proc. Steklov Inst. Math. 152 (1982), 97-98. MR 0603815 | Zbl 0502.52009

[16] Hadamard, J.: **Résolution d'une question relative aux déterminants**. Darboux Bull. (2) 17 (1893), 240-246 French \99999JFM99999 25.0221.02.

[17] Johnson, C. R.: **Inverse $M$-matrices**. Linear Algebra Appl. 47 (1982), 195-216. DOI 10.1016/0024-3795(82)90238-5 | MR 0672744 | Zbl 0488.15011

[18] Johnson, C. R., Smith, R. L.: **Inverse $M$-matrices II**. Linear Algebra Appl. 435 (2011), 953-983. DOI 10.1016/j.laa.2011.02.016 | MR 2807211 | Zbl 1218.15015

[19] Kalai, G., Ziegler, G. M., (Eds.): **Polytopes---Combinatorics and Computation**. DMV Seminar 29, Birkhäuser, Basel (2000). DOI 10.1007/978-3-0348-8438-9 | MR 1785290 | Zbl 0944.00089