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Wielandt-type bounds for primitive mappings of partially ordered sets

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Literature cited

  1. D. Rosenblatt, “On the graphs and asymptotic forms of finite Boolean relation matrices and stochastic matrices,” Naval Res. Logist. Quart.,4, No. 2, 151–167 (1957).

    Google Scholar 

  2. V. Pták, “On a certain combinatorial theorem and its applications to nonnegative matrices,” Czechoslovak Math. J.,8, (83), No. 4, 487–495 (1958).

    Google Scholar 

  3. J. Sedlacek, “On incidence matrices of directed graphs,” Casopis Pest. Mat.,84, No. 3, 303–316 (1959).

    Google Scholar 

  4. Yu. I. Lyubich, “Estimates for the optimal determination of indeterminate autonomous automata,” Sib. Mat. Zh.,5, No. 2, 337–355 (1964).

    Google Scholar 

  5. E. A. Bender and T. W. Tucker, “The exponents of strongly connected graphs,” Can. J. Math.,21., No. 4, 769–782 (1969).

    Google Scholar 

  6. S. Schwarz, “On a sharp estimation in the theory of binary relations on a finite set,” Czechoslovak Math. J.,20 (95), No. 4, 703–714 (1970).

    Google Scholar 

  7. S. Schwarz, “On the semigroup of binary relations on a finite set,” Czechoslovak Math. J.,20, (95), No. 4, 632–679 (1970).

    Google Scholar 

  8. H. Wielandt, “Unzerlegbare, nicht negative Matrizen,” Math. Z.,52, No. 5, 642–648 (1950).

    Google Scholar 

  9. J. C. Holladay and R. S. Varga, “On powers of nonnegative matrices,” Proc. Am. Math. Soc.,9, No. 4, 631–634 (1958).

    Google Scholar 

  10. M. A. Perles, “Critical exponents of convex sets,” in: Proceedings of the Colloquium on Convexity (Copenhagen, 1965), Københavns Univ. Mat. Inst., Copenhagen (1967), pp. 221–228.

    Google Scholar 

  11. S. Schwarz, “A new approach to some problems in the theory of nonnegative matrices,” Can. J. Math.,16, (91), No. 2, 274–284 (1966).

    Google Scholar 

  12. J. Mařík and V. Pták, “Norms, spectra and combinatorial properties of matrices,” Czechoslovak Math. J.,10, (85), No. 2, 181–196 (1960).

    Google Scholar 

  13. Yu. I. Lyubich and M. I. Tabachnikov, “On a theorem of Marik and Ptak,” Sib. Mat. Zh.,10, No. 2, 470–473 (1969).

    Google Scholar 

  14. Yu. I. Lyubich and M. I. Tabachnikov, “Subharmonic functions on a directed graph,” Sib. Mat. Zh.,10, No. 3, 600–613 (1969).

    Google Scholar 

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UkrkommunNIIproekt. Translated from Matematicheskie Zametki, Vol. 45, No. 6, pp. 30–35, June, 1989.

The author is grateful to Yu. I. Lyubich for his constant interest.

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Grinberg, V.S. Wielandt-type bounds for primitive mappings of partially ordered sets. Mathematical Notes of the Academy of Sciences of the USSR 45, 450–454 (1989). https://doi.org/10.1007/BF01158232

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