We show a simple method to generate polyominoes and polyiamonds that produce isohedral tilings with p3, p4 or p6 rotational symmetry by using n line segments between lattice points on a regular hexagonal, square and triangular lattice, respectively. We exhibit all possible tiles generated by this algorithm up to n = 9 for p3, n = 8 for p4, and n = 13 for… (More)
We describe computer algorithms that can enumerate and display, for a given n > 0 (in theory, of any size), all n-ominoes, n-iamonds, and n-hexes that can tile the plane using only rotations; these sets necessarily contain all such tiles that are fundamental domains for p4, p3, and p6 isohedral tilings. We display the outputs for small values of n. This… (More)
The tar and tsr genes of E. coli encode functionally analogous transducer proteins that mediate two distinct classes of chemotactic response. The tap gene lies adjacent to tar, and is thought to encode another transducer protein. We present here the complete nucleotide sequence of the tar-tap region of the E. coli genome, together with a comparative… (More)
Received (received date) Revised (revised date) Communicated by (Name) We describe computer algorithms that produce the complete set of isohedral tilings by n-omino or n-iamond tiles in which the tiles are fundamental domains and the tilings have 3-, 4-, or 6-fold rotational symmetry. The symmetry groups of such tilings are of types p3, p31m, p4, p4g, and… (More)
Some classes of I-factorizations of complete graphs are known. They are GK 2n , AK 2n , W K 2n and their variations, and automorphism-free I-factorizations. In this paper, for any positive integer t, we construct new I-factorizations N t K 2n which are defined for all 2n with 2n ~ 6t. They also have some variations.