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.
Kupavskii,Delta-system method: a survey
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Large t-intersecting families of k-subspaces in n-space (n ≥ 2k+1) admit a low-dimensional governing structure, enabling analogues of several classical extremal results.
The maximum cardinality of a set M of vectors in {0,±1}^n with (m,m)=4 and pairwise inner products restricted to {-4,-3,-2,-1,0,3} is determined for all sufficiently large n.
Short proofs are supplied for three results on (n,k,L)-systems in the Johnson scheme, the central one being a proof of the Aljohani-Bamberg-Cameron conjecture that complementary systems whose sizes multiply to binom(n,k) must be a t-intersecting family and a Steiner system S(t,k,n) when n exceeds so
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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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Structure of $t$-Intersecting Families of Vector Spaces
Large t-intersecting families of k-subspaces in n-space (n ≥ 2k+1) admit a low-dimensional governing structure, enabling analogues of several classical extremal results.
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On the maximum number of vectors in $\{0,\pm1\}^n$ with forbidden inner products
The maximum cardinality of a set M of vectors in {0,±1}^n with (m,m)=4 and pairwise inner products restricted to {-4,-3,-2,-1,0,3} is determined for all sufficiently large n.
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Short proofs of three combinatorial results in the Johnson scheme
Short proofs are supplied for three results on (n,k,L)-systems in the Johnson scheme, the central one being a proof of the Aljohani-Bamberg-Cameron conjecture that complementary systems whose sizes multiply to binom(n,k) must be a t-intersecting family and a Steiner system S(t,k,n) when n exceeds so