9,628 research outputs found
The nonexistence of regular near octagons with parameters (s, t, t(2), t(3)) = (2,24,0,8)
Let S be a regular near octagon with s + 1 = 3 points per line, let t + 1 denote the constant number of lines through a given point of S and for every two points x and y at distance i is an element of {2, 3} from each other, let t(i) + 1 denote the constant number of lines through y containing a (necessarily unique) point at distance i - 1 from x. It is known, using algebraic combinatorial techniques, that (t(2), t(3), t) must be equal to either (0, 0, 1), (0, 0, 4), (0, 3, 4), (0, 8, 24), (1, 2, 3), (2, 6, 14) or (4, 20, 84). For all but one of these cases, there is a unique example of a regular near octagon known. In this paper, we deal with the existence question for the remaining case. We prove that no regular near octagons with parameters (s, t, t(2), t(3)) = (2, 24, 0, 8) can exist
Perspectives for proof unwinding by programming languages techniques
In this chapter, we propose some future directions of work, potentially
beneficial to Mathematics and its foundations, based on the recent import of
methodology from the theory of programming languages into proof theory. This
scientific essay, written for the audience of proof theorists as well as the
working mathematician, is not a survey of the field, but rather a personal view
of the author who hopes that it may inspire future and fellow researchers
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