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Linear relations in dissections into n-dimensional parallelepipeds

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Literature cited

  1. 1.

    R. Brooks, C. Smith, A. Stone, and W. Tutte, “The dissection of rectangles into squares,” Duke Math. J.,7, 312–340 (1940).

    Google Scholar 

  2. 2.

    N. Biggs, “Rectangulations,” Proc. Cambridge Philos. Soc.,65, No. 2, 399–408 (1969).

    Google Scholar 

  3. 3.

    J. Magiera, “Grafowa reprezentacja rozbic zewnetrznych prostokata na prostokaty,” Pr. Nauk. AE Wroclawiu, No. 164, 165–170 (1980).

    Google Scholar 

  4. 4.

    N. G. De Bruijn, “Filling boxes with bricks,” Am. Math. Mon.,76, No. 1, 37–40 (1969).

    Google Scholar 

  5. 5.

    G. Katona and D. Szasz, “Matching problems,” J. Combinatorial Theory (B),10, No. 1, 60–92 (1971).

    Google Scholar 

  6. 6.

    V. G. Pokrovskii, ”On dissection of the n-dimensional cube into congruent parallelepipeds,” Mat. Zametki,30, No. 6, 881–887 (1981).

    Google Scholar 

  7. 7.

    F. Barnes, “Algebraic theory of brick packing. II,” Discrete Math.,42, Nos. 2–3, 129–144 (1982).

    Google Scholar 

  8. 8.

    N. Bourbaki, Commutative Algebra, Addison-Wesley (1972).

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Translated from Matematicheskie Zametki, Vol. 37, No. 6, pp. 901–907, June, 1985.

In conclusion, I express my gratitude to V. V. Proizvolov for stating the problem.

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Pokrovskii, V.G. Linear relations in dissections into n-dimensional parallelepipeds. Mathematical Notes of the Academy of Sciences of the USSR 37, 493–496 (1985).

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