11/2015, Cambridge studies in advanced mathematics, ISBN 1107128447, Volume 149, 332

...–Rado Theorem, with a focus on algebraic methods. The authors begin by discussing well-known proofs of the EKR bound for intersecting families...

Hypergraphs | Intersection theory | Combinatorial analysis

Hypergraphs | Intersection theory | Combinatorial analysis

eBook

Discrete Applied Mathematics, ISSN 0166-218X, 08/2019, Volume 266, pp. 65 - 75

Let ℒ=(X,⪯) be a lattice. For P⊆X we say that P is t-intersecting if rank(x∧y)≥t for all x,y∈P. The seminal theorem...

Intersecting permutations | Erdős–Ko–Rado theorem | Bruhat lattice | MATHEMATICS, APPLIED | SYSTEMS | Erdos-Ko-Rado theorem | INTERSECTION-THEOREMS | Permutations | Theorems | Lattices

Intersecting permutations | Erdős–Ko–Rado theorem | Bruhat lattice | MATHEMATICS, APPLIED | SYSTEMS | Erdos-Ko-Rado theorem | INTERSECTION-THEOREMS | Permutations | Theorems | Lattices

Journal Article

Discrete Mathematics, ISSN 0012-365X, 06/2018, Volume 341, Issue 6, pp. 1749 - 1754

A set system F is intersecting if for any F,F′∈F, F∩F′≠∅. A fundamental theorem of Erdős, Ko and Rado states that if F is an intersecting family of r-subsets of [n]={1,…,n}, and n≥2r, then |F|≤n−1r−1...

05D05 | Hilton–Milner | Injective proof | Intersecting families | Shifting technique | Erdős–Ko–Rado | MATHEMATICS | INTERSECTION-THEOREMS | SYSTEMS | Erdos-Ko-Rado | HEREDITARY FAMILIES | SUB-FAMILIES | Hilton-Milner | FINITE SETS

05D05 | Hilton–Milner | Injective proof | Intersecting families | Shifting technique | Erdős–Ko–Rado | MATHEMATICS | INTERSECTION-THEOREMS | SYSTEMS | Erdos-Ko-Rado | HEREDITARY FAMILIES | SUB-FAMILIES | Hilton-Milner | FINITE SETS

Journal Article

Discrete Mathematics, ISSN 0012-365X, 10/2017, Volume 340, Issue 10, pp. 2516 - 2527

.... We give versions of this kind for the selection theorem of Bárány, the existence of weak epsilon-nets for convex sets and the (p,q...

Helly theorem | Weak epsilon-net | Volume optimization | Tverberg theorem | Intersection of convex sets | ([formula omitted]) theorem | (p,q) theorem | FRACTIONAL HELLY THEOREM | NUMBERS | CONVEX-SETS | F-VECTORS | MATHEMATICS | ECKHOFF CONDITIONS | FAMILIES | BODIES | POINT | (p, q) theorem | LATTICE

Helly theorem | Weak epsilon-net | Volume optimization | Tverberg theorem | Intersection of convex sets | ([formula omitted]) theorem | (p,q) theorem | FRACTIONAL HELLY THEOREM | NUMBERS | CONVEX-SETS | F-VECTORS | MATHEMATICS | ECKHOFF CONDITIONS | FAMILIES | BODIES | POINT | (p, q) theorem | LATTICE

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 2017, Volume 369, Issue 2, pp. 1147 - 1162

We give a new proof of the Frankl-Rodl theorem on forbidden intersections, via the probabilistic method of dependent random choice...

MATHEMATICS | NUMBER | INEQUALITIES | INTERSECTIONS

MATHEMATICS | NUMBER | INEQUALITIES | INTERSECTIONS

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2016, Volume 2016, Issue 1, pp. 1 - 13

In this research, a multihierarchical methodology works by taking a whole intersection property to establish a fixed point theorem...

58C06 | whole intersection | fixed points | Mathematical and Computational Biology | 90C47 | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | minimax theorems | Multilayers | Minimax technique | Theorems | Fixed points (mathematics) | Mapping | Vector spaces | Intersections

58C06 | whole intersection | fixed points | Mathematical and Computational Biology | 90C47 | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | minimax theorems | Multilayers | Minimax technique | Theorems | Fixed points (mathematics) | Mapping | Vector spaces | Intersections

Journal Article

Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 01/2016, Volume 137, pp. 64 - 78

...) family, this gives us a random analogue of the Erdős–Ko–Rado theorem.

Transference | Intersecting families | Stability | Random graphs | RANDOM HYPERGRAPHS | SUBSETS | ARITHMETIC PROGRESSIONS | RAMSEY PROPERTIES | MATHEMATICS | INTERSECTION-THEOREMS | FAMILIES | SYSTEMS | EXTREMAL SUBGRAPHS | FINITE SETS

Transference | Intersecting families | Stability | Random graphs | RANDOM HYPERGRAPHS | SUBSETS | ARITHMETIC PROGRESSIONS | RAMSEY PROPERTIES | MATHEMATICS | INTERSECTION-THEOREMS | FAMILIES | SYSTEMS | EXTREMAL SUBGRAPHS | FINITE SETS

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 11/2019, Volume 129, Issue 11, pp. 4791 - 4836

Under certain mild conditions, some limit theorems for functionals of two independent Gaussian processes are obtained...

Pairing technique | Chaining argument | Method of moments | Gaussian processes | Limit theorem | INTERSECTION LOCAL-TIMES | FRACTIONAL BROWNIAN MOTIONS | STATISTICS & PROBABILITY | ALEATORY WALKS

Pairing technique | Chaining argument | Method of moments | Gaussian processes | Limit theorem | INTERSECTION LOCAL-TIMES | FRACTIONAL BROWNIAN MOTIONS | STATISTICS & PROBABILITY | ALEATORY WALKS

Journal Article

Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 04/2018, Volume 155, pp. 157 - 179

.... Thus, this problem may be seen as an extension of the classical Erdős–Ko–Rado theorem. Rather surprisingly there is a phase transition in the behaviour of the maximum at n...

[formula omitted]-vectors | Erdos–Ko–Rado theorem | Antipodal vectors | Intersecting family | {0,±1}-vectors | MATHEMATICS | CHROMATIC-NUMBERS | SPACES | BOUNDS | INTERSECTION-THEOREMS | INDEPENDENCE NUMBERS | DISTANCE GRAPHS | Erdos-Ko-Rado theorem | VERTICES | {0, +/- 1}-vectors

[formula omitted]-vectors | Erdos–Ko–Rado theorem | Antipodal vectors | Intersecting family | {0,±1}-vectors | MATHEMATICS | CHROMATIC-NUMBERS | SPACES | BOUNDS | INTERSECTION-THEOREMS | INDEPENDENCE NUMBERS | DISTANCE GRAPHS | Erdos-Ko-Rado theorem | VERTICES | {0, +/- 1}-vectors

Journal Article

Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 04/2018, Volume 155, pp. 493 - 502

.... Hilton and Milner proved a strong stability result for the celebrated Erdős–Ko–Rado theorem: when n>2k, every non-trivial intersecting family of k-subsets...

Erdős–Ko–Rado theorem | Intersecting families | Hilton–Milner theorem | MATHEMATICS | Hilton-Milner theorem | BOUNDS | KO-RADO THEOREM | INTERSECTION-THEOREMS | FAMILIES | HYPERGRAPH | MATCHING CONJECTURE | SYSTEMS | Erdds-Ko-Rado theorem | FINITE SETS

Erdős–Ko–Rado theorem | Intersecting families | Hilton–Milner theorem | MATHEMATICS | Hilton-Milner theorem | BOUNDS | KO-RADO THEOREM | INTERSECTION-THEOREMS | FAMILIES | HYPERGRAPH | MATCHING CONJECTURE | SYSTEMS | Erdds-Ko-Rado theorem | FINITE SETS

Journal Article

Advances in Mathematics, ISSN 0001-8708, 04/2019, Volume 347, pp. 859 - 903

We prove the Relative Hard Lefschetz theorem and the Relative Hodge-Riemann bilinear relations for combinatorial intersection cohomology sheaves on fans.

Fans | Relative Hard Lefschetz theorem | Toric varieties | MATHEMATICS | INTERSECTION COHOMOLOGY

Fans | Relative Hard Lefschetz theorem | Toric varieties | MATHEMATICS | INTERSECTION COHOMOLOGY

Journal Article

Set-Valued and Variational Analysis, ISSN 1877-0533, 3/2019, Volume 27, Issue 1, pp. 119 - 128

We are concerned in this note with the extension of Cantor’s intersection theorem to C(K) spaces...

46E15 | Analysis | Intersection property | Hausdorff convergence | Primary 52A05 | Secondary 46J10 | Mathematics | C ( K ) space | Order interval | Extremely disconnected compact | Optimization | MATHEMATICS, APPLIED | BANACH-SPACES | NESTED SEQUENCES | CONVEX-SETS | C(K) space

46E15 | Analysis | Intersection property | Hausdorff convergence | Primary 52A05 | Secondary 46J10 | Mathematics | C ( K ) space | Order interval | Extremely disconnected compact | Optimization | MATHEMATICS, APPLIED | BANACH-SPACES | NESTED SEQUENCES | CONVEX-SETS | C(K) space

Journal Article

Computational Geometry: Theory and Applications, ISSN 0925-7721, 01/2018, Volume 67, pp. 1 - 1

Journal Article

Advances in Applied Probability, ISSN 0001-8678, 6/2014, Volume 46, Issue 2, pp. 348 - 364

... integrals with respect to the compensated Poisson process. Also, we present a multivariate central limit theorem for a vector whose components admit a finite chaos expansion of the type of a Poisson U-statistic...

Stochastic Geometry and Statistical Applications | Even numbers | Central limit theorem | Approximation | Cardinality | Chaos theory | Mathematical integrals | Mathematical moments | Mathematical functions | Random variables | Poisson process | Poisson flat process | GAUSSIAN FLUCTUATIONS | Wiener-Ito chaos expansion | STATISTICS & PROBABILITY | Berry-Esseen-type bound | stochastic geometry | U-STATISTICS | SPACE | central limit theorem | multiple Wiener-Ito integral | intersection process | product formula

Stochastic Geometry and Statistical Applications | Even numbers | Central limit theorem | Approximation | Cardinality | Chaos theory | Mathematical integrals | Mathematical moments | Mathematical functions | Random variables | Poisson process | Poisson flat process | GAUSSIAN FLUCTUATIONS | Wiener-Ito chaos expansion | STATISTICS & PROBABILITY | Berry-Esseen-type bound | stochastic geometry | U-STATISTICS | SPACE | central limit theorem | multiple Wiener-Ito integral | intersection process | product formula

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2020, Volume 373, Issue 3, pp. 1501 - 1527

... and deduce that Howson's theorem holds for the Sylow subgroups of the absolute Galois group of a number field...

MATHEMATICS | HANNA-NEUMANN CONJECTURE | INTERSECTION | FINITELY GENERATED SUBGROUPS | GALOIS-GROUPS | FREE-PRODUCTS | PROPERTY | DEMUSKIN GROUPS | RANK | INDEX

MATHEMATICS | HANNA-NEUMANN CONJECTURE | INTERSECTION | FINITELY GENERATED SUBGROUPS | GALOIS-GROUPS | FREE-PRODUCTS | PROPERTY | DEMUSKIN GROUPS | RANK | INDEX

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 06/2016, Volume 18, Issue 3, p. 1550043

.... With this particular setting in mind, we prove a general correspondence theorem for enumerative problems which are defined via “evaluation maps...

Tropical geometry | Correspondence theorems | Algebraic geometry | FANS | MATHEMATICS | MATHEMATICS, APPLIED | correspondence theorems | VARIETIES | tropical geometry | CURVES | GEOMETRY | INTERSECTIONS | Mathematics - Algebraic Geometry

Tropical geometry | Correspondence theorems | Algebraic geometry | FANS | MATHEMATICS | MATHEMATICS, APPLIED | correspondence theorems | VARIETIES | tropical geometry | CURVES | GEOMETRY | INTERSECTIONS | Mathematics - Algebraic Geometry

Journal Article

Advances in applied probability, ISSN 0001-8678, 06/2014, Volume 46, Issue 2, pp. 348 - 364

... integrals with respect to the compensated Poisson process. Also, we present a multivariate central limit theorem for a vector whose components admit a finite chaos expansion of the type of a Poisson U-statistic...

Stochastic Geometry and Statistical Applications | Central limit theorem | Intersection process | Poisson flat process | Product formula | Stochastic geometry;Wiener-Itǒ chaos expansion | Integral | Berry-Esseen-type bound | Multiple Wiener-Itǒ | Poisson process | 60D05 | 60G55 | Wiener-Ito chaos expansion | stochastic geometry | central limit theorem | integral | 60H07 | multiple Wiener-Ito | intersection process | 60F05 | product formula

Stochastic Geometry and Statistical Applications | Central limit theorem | Intersection process | Poisson flat process | Product formula | Stochastic geometry;Wiener-Itǒ chaos expansion | Integral | Berry-Esseen-type bound | Multiple Wiener-Itǒ | Poisson process | 60D05 | 60G55 | Wiener-Ito chaos expansion | stochastic geometry | central limit theorem | integral | 60H07 | multiple Wiener-Ito | intersection process | 60F05 | product formula

Journal Article

Geometry and Topology, ISSN 1465-3060, 2018, Volume 22, Issue 1, pp. 105 - 156

We prove central limit theorems for the random walks on either the mapping class group of a closed, connected, orientable, hyperbolic surface, or on Out (F (N...

Central limit theorem | Mapping class groups | Out(F | Outer automorphism groups | Random walks on groups | MATHEMATICS | HYPERBOLIC GROUPS | COMPLEX | R-TREES | BOUNDARY | AUTOMORPHISMS | TEICHMULLER SPACE | INTERSECTION NUMBER | OUTER-SPACE | RANDOM MATRICES | GEOMETRY

Central limit theorem | Mapping class groups | Out(F | Outer automorphism groups | Random walks on groups | MATHEMATICS | HYPERBOLIC GROUPS | COMPLEX | R-TREES | BOUNDARY | AUTOMORPHISMS | TEICHMULLER SPACE | INTERSECTION NUMBER | OUTER-SPACE | RANDOM MATRICES | GEOMETRY

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 10/2016, Volume 181, Issue 2, pp. 451 - 471

In this paper we present some extensions of the Ailon–Rudnick theorem, which says that if $$f,g\in \mathbb {C}[T]$$ f , g ∈ C [ T ] , then $$\gcd (f^n-1,g^m-1)$$ gcd ( f n - 1 , g m - 1...

Mathematics, general | Mathematics | Greatest common divisor | Polynomials | 11D61 | 11R58 | MATHEMATICS | ABELIAN-VARIETIES | FINITE-FIELDS | VOJTAS CONJECTURE | EQUATIONS | TORSION | GREATEST COMMON DIVISORS | UNLIKELY INTERSECTIONS | POINTS | MULTIPLICATIVE GROUPS

Mathematics, general | Mathematics | Greatest common divisor | Polynomials | 11D61 | 11R58 | MATHEMATICS | ABELIAN-VARIETIES | FINITE-FIELDS | VOJTAS CONJECTURE | EQUATIONS | TORSION | GREATEST COMMON DIVISORS | UNLIKELY INTERSECTIONS | POINTS | MULTIPLICATIVE GROUPS

Journal Article

ARS MATHEMATICA CONTEMPORANEA, ISSN 1855-3966, 2019, Volume 16, Issue 1, pp. 257 - 276

.... This lead to an alternative statement and proof of Pappus's Theorem retrieving Pappus's and Hesse configurations of lines as special points in the complex projective Grassmannian...

MATHEMATICS | Grassmannian | MATHEMATICS, APPLIED | Discriminantal arrangements | Pappus's Theorem | intersection lattice

MATHEMATICS | Grassmannian | MATHEMATICS, APPLIED | Discriminantal arrangements | Pappus's Theorem | intersection lattice

Journal Article

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