Comparisons for numbers of complete mappings
Prikladnaâ diskretnaâ matematika, no. 4 (2014), pp. 13-20.

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For the numbers of standard complete mappings and for the numbers of standard strong complete mappings, comparisons modulo a prime number are obtained. The proofs of them are based on properties of some statistics and Euler's numbers on the related sets of permutations. For these sets, similar results taking into account the sign of permutations in them are also obtained.
Keywords: complete mappings, statistic, Euler's numbers, Wilson theorem, displacement of permutation.
Mots-clés : permutation
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L. N. Bondarenko; M. L. Sharapova. Comparisons for numbers of complete mappings. Prikladnaâ diskretnaâ matematika, no. 4 (2014), pp. 13-20. http://geodesic.mathdoc.fr/item/PDM_2014_4_a1/

[1] Hsiang J., Hsu D. F., Shieh Y. P., “On the hardness of counting problems of complete mappings”, Discrete Mathematics, 277 (2004), 87–100 | DOI | MR | Zbl

[2] Graham R. L., Lehmer D. H., “On the permanent of Schur's matrix”, J. Australian Math. Soc. Series A, 21, Part 4 (1976), 487–497 | DOI | MR | Zbl

[3] Bondarenko L. N., “Permanenty i “additivnye” zadachi perechisleniya perestanovok”, Materialy VII Mezhdunar. seminara “Diskretnaya matematika i ee prilozheniya” (29 yanvarya – 2 fevralya 2001 g.), Ch. III, Izd-vo tsentra prikladnykh issledovanii pri mekhaniko-matematicheskom fakultete MGU, M., 2001, 335–338

[4] Stenli R., Perechislitelnaya kombinatorika, v. 1, Mir, M., 1990, 440 pp. | MR

[5] Moser W. O. J., “A (modest) generalization of theorems of Wilson and Fermat”, Canadian Math. Bul., 33:2 (1990), 253–256 | DOI | MR | Zbl

[6] Melnikov I. G., Slavutskii I. Sh., “O dvukh zabytykh dokazatelstvakh zakona vzaimnosti”, Istoriya fiziko-matematicheskikh nauk, Trudy instituta istorii estestvoznaniya i tekhniki, 28, M., 1959, 201–218 | Zbl

[7] Aierlend K., Rouzen M., Klassicheskoe vvedenie v sovremennuyu teoriyu chisel, Mir, M., 1987, 416 pp. | MR

[8] Bondarenko L. N., Sharapova M. L., “Primenenie obobschennoi formuly Rodriga v kombinatornom analize”, Izv. vuzov. Povolzhskii region. Fiz.-mat. nauki, 2011, no. 4(20), 44–58

[9] Sloane N. J. A., The on-line encyclopedia of integer sequences, http://oeis.org/A003111

[10] Sloane N. J. A., The on-line encyclopedia of integer sequences, http://oeis.org/A003112