A Steiner triple system of order v (briefly STS(v)) is a pair (X, B), where X is a v-element set and B is a collection of 3-subsets of X (triples), such that every pair of X is contained in exactlyâ€¦ (More)

Completeness or primality for partial algebras on a finite universe A is defined in a way similar to full algebras. A universal completeness criterion reduces to finding the complete list of maximalâ€¦ (More)

A Steiner triple system of order v (briefly STS(v)) is a pair (X, ~ ) where X is a v-element set and ~ is a collection of 3-subsets of X (triples), such that every pair of X is contained in exactlyâ€¦ (More)

Hill [6] showed that the largest cap in PG(5, 3) has cardinality 56. Using this cap it is easy to construct a cap of cardinality 45 inAG(5, 3). Here we show that the size of a cap in AG(5, 3) isâ€¦ (More)

Let 2 = {0,1}. We show thatÂ Â the interval ofÂ Â partial clones containing the set of all selfdual monotonic partial functionsÂ Â is infinite on 2. We also study some partial clones in that interval.

Recent developments of universal algebra show the importance of clones as a tool of analysis and classification. A clone is a superposition closed set of finitary operations on a fixed finite set Aâ€¦ (More)