Decompositions resembling Pascal's triangle in binomial configurations arise from hyperplane selections in classes K where both the hyperplane and its deletion remain in K, with two additional such classes presented.
Binomial partial Steiner triple systems with complete graphs: structural problems
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abstract
In the paper we study the structure of hyperplanes of so called binomial partial Steiner triple systems (BSTS's, in short) i.e. of configurations with $\binom{n}{2}$ points and $\binom{n}{3}$ lines, each line of the size $3$. Consequently, a BSTS has $n-2$ lines through each of its points.
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math.CO 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Hyperplanes in Configurations, decompositions, and Pascal Triangle of Configurations
Decompositions resembling Pascal's triangle in binomial configurations arise from hyperplane selections in classes K where both the hyperplane and its deletion remain in K, with two additional such classes presented.