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Ordinary multiplication of natural numbers can be generalized to a ternary operation by considering discrete volumes of lattice hexagons. With this operation, a natural notion of ‘3-primality’ -primality with respect to ternary multiplication- is defined, and it turns out that there are very few 3-primes. They correspond to imaginary quadratic fiel...
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Context 1
... that if we put a 1 as an argument of this product, one of the pairs of sides of the hexagon degenerates to a single point and we instead have a parallelogram (see Figure 4). The discrete volume of this parallelogram is then just the value of the binary product of the other two arguments, so we observe ordinary multiplication as a specialization of the ternary product. ...
Context 2
... have seen that x, y, 1 = xy. Increasing the third argument by 1 adds a hooked strip of x + y − 1 points along two consecutive edges opposite to those with x and y points (see again Figure 4, where the argument increases from 1 to 2). This allows us to conclude the claimed equality, Scholars of symmetric polynomials will recognize (1) as an alternating sum of elementary symmetric polynomials, 3 ...
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