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Design theory is the subfield of combinatorics concerning the existence and construction of highly symmetric arrangements. Finite projective planes, latin squares, and Steiner triple systems are examples of designs.
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What is the largest number of k-element subsets of a given n-element set S such that…
Given a set S of n elements. What is the largest number of k-element subsets of S such that every pair of these subsets has at most one common element?