Proves that for sufficiently large n the maximum t-intersecting families in S_n are the fixed-point families F_{n,t,r}, resolving the Deza-Frankl problem asymptotically.
The Hajnal–Rothschild problem, arxiv:2502.06699
3 Pith papers cite this work. Polarity classification is still indexing.
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For t < c n the only maximal (t-1)-intersection-free families in GL(n,q) are the t-umvirates and their duals.
Largest s-matching-free families of permutations are characterized, with a Hilton-Milner type theorem and results for derangements.
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A Complete Intersection Theorem for Large Permutation Groups
Proves that for sufficiently large n the maximum t-intersecting families in S_n are the fixed-point families F_{n,t,r}, resolving the Deza-Frankl problem asymptotically.
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Forbidden Intersection Theorems for Matrix Spaces
For t < c n the only maximal (t-1)-intersection-free families in GL(n,q) are the t-umvirates and their duals.
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Matchings in permutations
Largest s-matching-free families of permutations are characterized, with a Hilton-Milner type theorem and results for derangements.