On the number of k-valued functions with given range of their subfunctions
by
Dimiter Stoichkov Kovachev
South-West University Neofit Rilsi
Coauthors: Iliya D. Gyudzhenov (South-West University “Neofit Rilski

Let M and R be sets of variables of a function where M is not a subset of R.

In this paper we generalize some of the results published in [1]. The number of n-variable k-valued functions is found which:

• Assume exactly b different values among k possible values and each subfunction of these functions with arguments from M assumes exactly a different values, where a is less than or equal to b.
• Assume exactly q different values of k possible values and the spectrum of M with respect to R for these functions is a singleton containing the element q.

The way of counting can also be used for constructing the functions under consideration.

[1] Dimiter. St. Kovachev, “n the number of some k-valued functions of n variables”, Union of Bulgarian Mathematician, MATHEMATICS AND EDUCATION IN MATHEMATICS, Proceedings of Thirtieth Spring Conference of the Union of Bulgarian Mathematicians, Borovets, April 8-11, 2001, pp. 176-181.

[2] D. St. Kovachev, “On the Number of Discrete Functions with a Given Range”, General Algebra and Applications, Proceedings of the “59th Workshop on General Algebra“, Potsdam 2000, edited by K. Denecke and H.-J. Vogel, pp. 125-134.

Date received: July 27, 2001