named after Emanuel Sperner, who published it in 1928. This result is sometimes called Sperner's lemma, but the name "Sperner's lemma" also refers to...

In mathematics, Sperner's lemma is a combinatorial result on colorings of triangulations, analogous to the Brouwer fixed point theorem, which is equivalent...

universities until 1974. Sperner's theorem, from 1928, says that the size of an antichain in the power set of an n-set (a Sperner family) is at most the...

system or irredundant set. Sperner families are counted by the Dedekind numbers, and their size is bounded by Sperner's theorem and the Lubell–Yamamoto–Meshalkin...

X—essentially {1, 2, …, n}—ordered by inclusion or, notationally, (2[n], ⊆). Sperner's theorem states that a maximum antichain of Bn has size at most width ⁡ ( B...

applications in combinatorics. In particular, it can be used to prove Sperner's theorem. Its name is also used for similar inequalities. Let U be an n-element...

isomorphic to the homology group Hn-1(∂M) by de Rham's theorem. The BFPT can be proved using Sperner's lemma. We now give an outline of the proof for the...

theory) Sperner's theorem (combinatorics) Stanley's reciprocity theorem (combinatorics) Star of David theorem (combinatorics) Stirling's theorem (mathematical...

has an incomplete proof. Sperner's theorem Clements, G. F.; Lindström, B. (1969), "A generalization of a combinatorial theorem of Macaulay", Journal of...

JSTOR 2320587 Jarvis, Tyler; Tanton, James (2004), "The Hairy Ball Theorem via Sperner's Lemma", American Mathematical Monthly, 111 (7): 599–603, doi:10...

that intersecting families of convex sets have a common intersection Sperner's theorem, an upper bound on families of pairwise non-nested sets Steiner system...

constraints). Mean value theorem Non-atomic measure Hairy ball theorem Sperner's lemma Weisstein, Eric W. "Bolzano's Theorem". MathWorld. Cates, Dennis...

Sperner property and Sperner posets are named after Emanuel Sperner, who proved Sperner's theorem stating that the family of all subsets of a finite set (partially...

which none contains any other? The latter question is answered by Sperner's theorem, which gave rise to much of extremal set theory. The types of questions...

Pigeonhole principle and double counting, Sperner's lemma Sperner's theorem, Erdős–Ko–Rado theorem and Hall's theorem Lindström–Gessel–Viennot lemma and the...

are not constrained. Hall's theorem can be proved (non-constructively) based on Sperner's lemma.: Thm.4.1, 4.2  The theorem has many applications. For...

which none contains any other? The latter question is answered by Sperner's theorem, which gave rise to much of extremal set theory. Another kind of example:...

Arrow's impossibility theorem is a key result in social choice theory showing that no ranked-choice procedure for group decision-making can satisfy the...

In mathematics, the Lusternik–Schnirelmann theorem, aka Lusternik–Schnirelmann–Borsuk theorem or LSB theorem, says as follows. If the sphere Sn is covered...

Mazurkiewicz. The KKM lemma can be proved from Sperner's lemma and can be used to prove the Brouwer fixed-point theorem. Let Δ n − 1 {\displaystyle \Delta _{n-1}}...

Show that a straight line can contain points of only two colours. Use Sperner's lemma to show that every triangulation of the square into triangles meeting...

point, but it doesn't describe how to find the fixed point (see also Sperner's lemma). For example, the cosine function is continuous in [−1, 1] and...

(3 December 2014). From Sperner's Lemma to Differential Equations in Banach Spaces : An Introduction to Fixed Point Theorems and their Applications. KIT...

refinement. A Sperner family is a set family in which none of the sets contains any of the others. Sperner's theorem bounds the maximum size of a Sperner family...

fruitful point of view in finding interesting new theorems. For example, there are q-analogs of Sperner's theorem and Ramsey theory. [citation needed] Let q...

In mathematics, the Borsuk–Ulam theorem states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points...

\lfloor {n/2}\rfloor }\approx 2^{n}\,{\frac {1}{\sqrt {n}}}} using Sperner's theorem. This bound is sharp; equality is attained when all vectors in S are...

are connected with a lot of important combinatorial theorems. The classic example is Sperner's theorem, which can be formulated as follows: For the power...

Nakayama's lemma Poincaré's lemma Riesz's lemma Schur's lemma Schwarz's lemma Sperner's lemma Urysohn's lemma Vitali covering lemma Yoneda's lemma Zorn's lemma...

Kakutani fixed-point theorem in his 1950 paper to prove existence of equilibria. His 1951 paper used the simpler Brouwer fixed-point theorem for the same purpose...