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Arithmetic problems of combinatorial analysis. (English. Russian original) Zbl 0831.05006
Math. Notes 55, No. 2, 173-177 (1994); translation from Mat. Zametki 55, No. 2, 102-108 (1994).
The author studies permutations of \({\mathcal S}_n\) with given cyclic structure. He estimates some arithmetic functions connected with the sets determining this cyclic structure. The number of solutions of a given equation, the number of equivalence classes of binary \(m \times n\) matrices, etc. are dealt with.
Reviewer: N.L.Manev (Sofia)
MSC:
05A15 Exact enumeration problems, generating functions
05A16 Asymptotic enumeration
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[1] J. Riordan, Introduction to Combinatorial Analysis [Russian translation], Inostrannaya Literatura, Moscow (1963). · Zbl 0106.24001
[2] E. A. Bender, ”Asymptotic methods in enumeration theory,” Enumeration Problems of Combinatorial Analysis [Russian translation], Mir, Moscow (1979), pp. 266–310.
[3] A. I. Pavlov, Trudy MIAN,207.
[4] A. I. Pavlov, ”On the number and cyclic structure of permutations of certain classes,” Mat. Sbornik,124, No. 4, 536–556 (1984). · Zbl 0559.20005
[5] Yu. V. Bolotnikov, V. N. Sachkov, and V. E. Tarakonov, ”Some classes of random quantities on permutation cycles,” Mat. Sbornik,108, No. 1, 91–104 (1979).
[6] M. P. Mineev and A. I. Pavlov, ”On the number of permutations of special type,” Mat. Sbornik,99, No. 3, 486–476 (1976). · Zbl 0422.20005
[7] P. Turan, ”On some connections between combinatorics and group theory,” Coll. Math. Soc. Janoc Bolyai 4, P. Erdös and V. T. Soc. (Eds.), North-Holland, Amsterdam (1970).
[8] J. Blum, ”Enumeration of the square permutation inS n ,” J. Comb. Theory,A17, No. 2, 156–161 (1974). · Zbl 0288.05005 · doi:10.1016/0097-3165(74)90002-8
[9] A. I. Pavlov, ”On the number of solutions to the equationx k =a in the symmetric group,” Mat. Sbornik,112, No. 3, 380–395 (1980). · Zbl 0438.20002
[10] H. S. Wilf, ”The asymptotics ofe P(z) and the number of elements of each order inS n ,” Bull. Amer. Math. Soc.,15, No. 2, 228–232 (1986). · Zbl 0613.05007 · doi:10.1090/S0273-0979-1986-15486-8
[11] A. I. Pavlov, ”The asymptotics of the number of solutions to a particular system of equations in permutations,” Diskr. Matem.,1, No. 2, 143–154 (1989). · Zbl 0728.05006
[12] M. Harrison, ”On the number of classes of binary matrices,” IEEE Trans. Comp.,C-22, No. 12 (1973). · Zbl 0288.94014
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