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Some achievements in Discrete Mathematics

1.
Proof of Yamamoto's supposition (1956) on permanents. DAN of the Ukraine 11 (1988), 32-35.
2.
Full completion of the Metropolis-Stein-Stein-Minc theory of permanents of circulants. J. of Soviet Mathematics (New York) v.61, no. 4 (1992), 2272-2317.
3.
Sums of subpermanents of linear spans of substitution matrices. Discrete Maths. Appl. (Utrecht-Tokyo) v.2, no. 2 (1992), 201-218.
4.
Counterexample to a conjecture of K. Balasubramanian on permanents (Linear Algebra Appl. (1990), 131, 125-129), Discrete Maths. Appl. (Utrecht-Tokyo) v.3, no. 3 (1993), 229-263 (see pp 249-250).
5.
Solution of Grinstein problem (1978) for symmetrical matrices and algorithm of solution of full Grinstein problem (the same journal, pp. 258-259).
6.
Wide generalization of classic Riordan's formula for reduced 3-row Latin rectangles (the same journal, pp. 255-257).
7.
Development of an analog of rook technique for constructing cyclic indicator of arbitrary (0,1) quadratic matrix (Izv. Vuzov, Sev. Kavk. Region, nature sc., 4 (1996), 21-28).
8.
Counterexample for Nicol formula of number of solutions of the congruence . It is found another explicit formula (the same journal, 2 (1997), 25-37).
9.
For the first time it is constructed by V. Shevelev an arithmetics in the base of Fermi-Dirac statistics (when each "cell" could be filled not more than 1 subject) (Izv. of Sev-Kavk Sc. Center, Maths. N.2 (1981), 13-17).

Development: Izv. Vuzov, Sev-Kavk region, nature sc. 4 (1996), 28-42.

10.
Theorem: If all different from 1 divisors of n are sufficiently large, then the number of permutations of elements with prescribed sequence of "up" and "down" points is equal to +1 or with the choice of +1 or -1 according to the Morse (0,1) sequence (the same journal, 4, (1996), 20-24).
11.
Proof of some Ramanujan formulas, which he left without any proof ("Mathematical World" (AMS), 14, 139-144 (1999)).
12.
Article in the Theory of Codes (together with Prof. Simon Litsyn (Tel-Aviv University)): On ensembles of low-density parity-check codes: asymptotic distance distributions. IEEE Transactions on Information Theory, 48, no. 4 (2002), 887-908.
The full list of publications of Prof. Shevelev includes more than 150 articles.
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Sven Reichard
2002-07-04