Results 41 to 50 of about 13,803 (191)

Generalized Ramsey–Turán density for cliques

Forum of Mathematics, Sigma
We study the generalized Ramsey–Turán function $\mathrm {RT}(n,K_s,K_t,o(n))$ , which is the maximum possible number of copies of $K_s$ in an n-vertex $K_t$ -free graph with independence number $o(n)$ . The case when $s=2$
Jun Gao, Suyun Jiang, Hong Liu, Maya Sankar   +3 more
doaj   +1 more source

On the extremal combinatorics of the hamming space

Journal of Combinatorial Theory, Series A, 1995
In \(n\)-dimensional Hamming space three points are on a line, if they satisfy the triangle inequality with equality. The paper introduces the following problem: How many different points can be found in the Hamming space so that no three of them are on a line (that is they are in general position)? This maximum value is \(A(n)\). The paper surveys the
openaire   +5 more sources

Shattered Sets and the Hilbert Function [PDF]

, 2016
We study complexity measures on subsets of the boolean hypercube and exhibit connections between algebra (the Hilbert function) and combinatorics (VC theory). These connections yield results in both directions.
Moran, Shay, Rashtchian, Cyrus
core   +1 more source

Extremal Permanents of Laplacian Matrices of Unicyclic Graphs

Axioms
The extremal problem of Laplacian permanents of graphs is a classical and challenging topic in algebraic combinatorics, where the inherent #P-complete complexity of permanent computation renders this pursuit particularly intractable.
Tingzeng Wu, Xiuhong Wang, Xiangshuai Dong   +2 more
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Additive energies on discrete cubes

Discrete Analysis, 2023
One definition of additive combinatorics is that it is the study of subsets of (usually Abelian) groups. Two much studied parameters associated with a subset $A$ are the size of its sumset $A+A=\{a+b:a,b\in A\}$ (or the product set $A.A=\{a.b:a,b\in A\}$
Jaume de Dios Pont, Rachel Greenfeld, Paata Ivanisvili, José Madrid   +3 more
doaj   +1 more source

Extremes of the internal energy of the Potts model on cubic graphs [PDF]

, 2017
We prove tight upper and lower bounds on the internal energy per particle (expected number of monochromatic edges per vertex) in the anti-ferromagnetic Potts model on cubic graphs at every temperature and for all $q \ge 2$.
Davies, Ewan, Jenssen, Matthew, Perkins, Will, Roberts, Barnaby   +3 more
core   +2 more sources

A proof of the Elliott–Rödl conjecture on hypertrees in Steiner triple systems

Forum of Mathematics, Sigma
Hypertrees are linear hypergraphs where every two vertices are connected by a unique path. Elliott and Rödl conjectured that for any given $\mu>0$ , there exists $n_0$ such that the following holds.
Seonghyuk Im, Jaehoon Kim, Joonkyung Lee, Abhishek Methuku   +3 more
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Forbidden intersection problems for families of linear maps

Discrete Analysis, 2023
Forbidden intersection problems for families of linear maps, Discrete Analysis 2023:19, 32 pp. A central problem in extremal combinatorics is to determine the maximal size of a set system given constraints on the sizes of the sets in the system and on ...
David Ellis, Guy Kindler, Noam Lifshitz
doaj   +1 more source

Gowers norms for automatic sequences

Discrete Analysis, 2023
Gowers norms for automatic sequences, Discrete Analysis 2023:4, 62 pp. There are several situations in additive and extremal combinatorics where it is useful to decompose an object $X$ into a "structured" part $S(X)$ and a "quasirandom" part $Q(X)$.
Jakub Byszewski, Jakub Konieczny, Clemens Müllner   +2 more
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An efficient container lemma

Discrete Analysis, 2020
An efficient container lemma, Discrete Analysis 2020:17, 56 pp. The hypergraph container lemma, discovered independently in 2012 by David Saxton and Andrew Thomason, and by József Balogh, Robert Morris and Wojciech Samotij, is an extremely powerful tool
Jozsef Balogh, Wojciech Samotij
doaj   +1 more source