Results 81 to 90 of about 887,124 (211)

SPERNER THEOREMS FOR UNRELATED COPIES OF POSETS AND GENERATING DISTRIBUTIVE LATTICES

Ural Mathematical Journal
For a finite poset (partially ordered set) \(U\) and a natural number \(n\), let \(S(U,n)\) denote the largest number of pairwise unrelated copies of  \(U\) in the powerset lattice (AKA subset lattice) of an \(n\)-element set.
Gábor Czédli
doaj   +1 more source

Hamilton cycles in graphs and hypergraphs: an extremal perspective [PDF]

, 2014
As one of the most fundamental and well-known NP-complete problems, the Hamilton cycle problem has been the subject of intensive research. Recent developments in the area have highlighted the crucial role played by the notions of expansion and quasi ...
Kühn, Daniela, Osthus, Deryk
core   +1 more source

On extremal problems associated with random chords on a circle

Mathematika, Volume 71, Issue 4, October 2025.
Abstract Inspired by the work of Karamata, we consider an extremization problem associated with the probability of intersecting two random chords inside a circle of radius r,r∈(0,1]$r, \, r \in (0,1]$, where the endpoints of the chords are drawn according to a given probability distribution on S1$\mathbb {S}^1$.
Cynthia Bortolotto, João P. G. Ramos
wiley   +1 more source

Discrete Extremal Length and Cube Tilings in Finite Dimensions

, 2014
Extremal length is a conformal invariant that transfers naturally to the discrete setting, giving square tilings as a natural combinatorial analog of conformal mappings. Recent work by S.
Wood, William E.
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The structure of sets with cube‐avoiding sumsets

Mathematika, Volume 71, Issue 4, October 2025.
Abstract Suppose G$G$ is a finite abelian group, Z0⊂G$Z_0 \subset G$ is not contained in any strict coset in G$G$, and E,F$E,F$ are dense subsets of Gn$G^n$ such that the sumset E+F$E+F$ avoids Z0n$Z_0^n$. We show that E$E$ and F$F$ are almost entirely contained in sets defined by a bounded number of coordinates, that is, sets E′×GIc$E^{\prime } \times
Thomas Karam, Peter Keevash
wiley   +1 more source

Quantitative bounds in the polynomial Szemerédi theorem: the homogeneous case

Discrete Analysis, 2017
Quantitative bounds in the polynomial Szemerédi theorem: the homogeneous case, Discrete Analysis 2017:5, 34 pp. Szemerédi's theorem, proved in 1975, asserts that for every positive integer $k$ and every $\delta>0$ there exists $n$ such that every subset
Sean Prendiville
doaj   +1 more source

Linear trees in uniform hypergraphs [PDF]

, 2013
Given a tree T on v vertices and an integer k exceeding one. One can define the k-expansion T^k as a k-uniform linear hypergraph by enlarging each edge with a new, distinct set of (k-2) vertices. Then T^k has v+ (v-1)(k-2) vertices. The aim of this paper
Furedi, Zoltan
core  

Geometric inequalities, stability results and Kendall's problem in spherical space

Mathematika, Volume 71, Issue 4, October 2025.
Abstract In Euclidean space, the asymptotic shape of large cells in various types of Poisson‐driven random tessellations has been the subject of a famous conjecture due to David Kendall. Since shape is a geometric concept and large cells are identified by means of geometric size functionals, the resolution of the conjecture is inevitably connected with
Daniel Hug, Andreas Reichenbacher
wiley   +1 more source

Quasirandom Cayley graphs

Discrete Analysis, 2017
Quasirandom Cayley graphs, Discrete Analysis 2017:6, 14 pp. An extremely important phenomenon in extremal combinatorics is that of _quasirandomness_: for many combinatorial structures, it is possible to identify a list of deterministic properties, each ...
David Conlon, Yufei Zhao
doaj   +1 more source

Tightening inequalities on volume‐extremal k$k$‐ellipsoids using asymmetry measures

Mathematika, Volume 71, Issue 4, October 2025.
Abstract We consider two well‐known problems: upper bounding the volume of lower dimensional ellipsoids contained in convex bodies given their John ellipsoid, and lower bounding the volume of ellipsoids containing projections of convex bodies given their Loewner ellipsoid.
René Brandenberg, Florian Grundbacher
wiley   +1 more source