zbMATH — the first resource for mathematics

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)
05A15 Exact enumeration problems, generating functions
05A16 Asymptotic enumeration
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.