union-closed sets conjecture, also known as Frankl’s conjecture, is an open problem in combinatorics posed by Péter Frankl in 1979. A family of sets is...

sets be bounded by an exponential function in k {\displaystyle k} for every fixed r > 2 {\displaystyle r>2} ? Frankl's union-closed sets conjecture –...

especially in extremal combinatorics. He is the author of the union-closed sets conjecture. Both of his parents were survivors of concentration camps and...

Erdős–Ko–Rado theorem Kruskal–Katona theorem Fisher's inequality Union-closed sets conjecture Jukna, Stasys (2011), Extremal Combinatorics, With Applications...

Dg is closed. This in turn is a special case of a general conjecture of Margulis on Lie groups. Borel showed in 1909 that the exceptional set of real...

sets. A set may be finite or infinite. There is a unique set with no elements, called the empty set; a set with a single element is a singleton. Sets...

set is the Zariski closure of the images of all non-constant holomorphic maps from C. Lang conjectured that the analytic and algebraic special sets are...

subsets; that is, any subset of a meagre set is meagre, and the union of countably many meagre sets is meagre. Meagre sets play an important role in the formulation...

theorem was known as Wagner's conjecture after the German mathematician Klaus Wagner, although Wagner said he never conjectured it. A weaker result for trees...

In geometry, Keller's conjecture is the conjecture that in any tiling of n-dimensional Euclidean space by identical hypercubes, there are two hypercubes...

S may equivalently be defined as the union of S and its boundary, and also as the intersection of all closed sets containing S. Intuitively, the closure...

analysis of Ricci flow, and proved the Poincaré conjecture and Thurston's geometrization conjecture, the former of which had been a famous open problem...

Thue–Morse sequence Tower of Hanoi Turán number Turing tarpit Union-closed sets conjecture Urn problems (probability) Vandermonde's identity Weighing matrices...

element in common; and a conjecture of Václav Chvátal that the largest intersecting family of any downward-closed family of sets is always achieved by a...

(2003) p.91 Foreman, Matthew (2002) Stationary sets, Chang's Conjecture and partition theory, in Set Theory (The Hajnal Conference) DIMACS Ser. Discrete...

this are the Kurepa conjecture and the Suslin conjecture. Both of these problems are known to be independent of Zermelo–Fraenkel set theory. By Kőnig's...

independent sets; bases or circuits; rank functions; closure operators; and closed sets or flats. In the language of partially ordered sets, a finite simple...

concept of open sets. If we change the definition of 'open set', we change what continuous functions, compact sets, and connected sets are. Each choice...

minor may be formed by gluing together simpler pieces, and Hadwiger's conjecture relating the inability to color a graph to the existence of a large complete...

mathematics Haboush's theorem, often still referred to as the Mumford conjecture, states that for any semisimple algebraic group G over a field K, and...

is the Green–Griffiths–Lang conjecture: if X is a complex projective variety of general type, then there should be a closed algebraic subset Y not equal...

the existence of particular sets defined from other sets. For example, the axiom of pairing says that given any two sets a {\displaystyle a} and b {\displaystyle...

properties of sets leads to the contradiction of Russell's paradox. This has been resolved by elaborating the rules that are allowed for manipulating sets. This...

that any cover of the plane by five congruent closed sets contains a unit distance in one of the sets. Hadwiger proved a theorem characterizing eutactic...

the Cantor set is uncountable but has Lebesgue measure 0. Since the Cantor set is the complement of a union of open sets, it itself is a closed subset of...

the theory of symplectic topology as a distinct discipline. The Arnold conjecture on the number of fixed points of Hamiltonian symplectomorphisms and Lagrangian...

classical Hilbert irreducibility theorem. A thin set, in general, is a subset of a finite union of thin sets of types I and II . The terminology thin may...

these sets be non-empty is needed because sets in a partition are by definition required to be non-empty. Let S {\displaystyle S} be a closed subset...

finite generation of the set of rational points as opposed to finiteness). In 2001, the proof of the local Langlands conjectures for GLn was based on the...

Introduction to Set Theory, 3rd edition, Chapter 11, Section 3. Mark Howard, Applications of Fodor's Lemma to Vaught's Conjecture. Ann. Pure and Appl...