graph homomorphism. There is a connection between homomorphism densities and subgraph densities, which is elaborated on below. The edge density of a graph...

Hölder's inequality can be used to derive homomorphism inequalities. A major open problem relating homomorphism densities is Sidorenko's conjecture, which states...

graph homomorphisms from a fixed graph are asymptotically equal. Given two graphs F {\displaystyle F} and G {\displaystyle G} , the homomorphism density t...

applications in homomorphism density and related topics. Roughly, they formalize the notion of adding and multiplying homomorphism densities and set up a...

Then, for a homomorphism f : G → H, (f(u),f(v)) is an arc (directed edge) of H whenever (u,v) is an arc of G. There is an injective homomorphism from G to...

to a branch of extremal graph theory concerning inequalities in homomorphism densities. Roughly speaking, F {\displaystyle F} is a common graph if it "commonly"...

inequality about graph homomorphism densities in graphons. The conjectured inequality can be interpreted as a statement that the density of copies of H {\displaystyle...

{\displaystyle K_{a}} . Turan's theorem states that if a graph has edge homomorphism density strictly above 1 − 1 r − 1 {\displaystyle 1-{\frac {1}{r-1}}} , it...

verify that a sequence of graphs is quasi-random by just checking the homomorphism density of a single graph. There is a second definition of forcing graphs...

scalar of the cut distance between two graphs is correlated to the homomorphism density between them and H {\displaystyle H} . Whenever we have an ϵ {\displaystyle...

vertices at distance two as at distance one? Sidorenko's conjecture on homomorphism densities of graphs in graphons Tutte's conjectures: every bridgeless graph...

is equivalent to the surjectivity of the homomorphism R → M that sends r to xr. The kernel of this homomorphism is a right ideal I of R, and a standard...

map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V → W {\displaystyle...

vector Kernel (category theory), a generalization of the kernel of a homomorphism Kernel (set theory), an equivalence relation: partition by image under...

{\displaystyle \rho } be a representation of GL(n) on W (that is, a group homomorphism ρ : GL ( n ) → GL ( W ) {\displaystyle \rho :{\text{GL}}(n)\to {\text{GL}}(W)}...

again independently by Bill Parry in 1960. The map can be obtained as a homomorphism on the Bernoulli process. Let Ω = { H , T } N {\displaystyle \Omega =\{H...

representations of Diffx1(M)? Let's use the fact that if we have a group homomorphism φ:G → H, then if we have a H-representation, we can obtain a restricted...

defining a crossed homomorphism c of G into M can be expressed in terms of standard homomorphisms of groups: it is encoded in a homomorphism 𝜙 of G into the...

{\displaystyle X} to the locale Y {\displaystyle Y} is given by a frame homomorphism O ( Y ) → O ( X ) {\displaystyle O(Y)\to O(X)} . Every topological space...

homological dimension homomorphism For two left R {\displaystyle R} -modules M 1 , M 2 {\displaystyle M_{1},M_{2}} , a group homomorphism ϕ : M 1 → M 2 {\displaystyle...

{\displaystyle \Phi :A\to B(H),} there exists a Hilbert space K and a unital *-homomorphism π : A → B ( K ) {\displaystyle \pi :A\to B(K)} such that Φ ( a ) = V...

about these relations. This is related to the concept of isomorphism, or homomorphism in mathematics.: 43  Sometimes certain geometric properties (such as...

isomorphism gives a homomorphism AE → abelianization of E/F, and taking the limit over all open subgroups F gives a homomorphism AE → abelianization of...

group homomorphisms; it is the direct product of the fundamental homomorphism on SO ( n ) {\displaystyle {\text{SO}}(n)} with the trivial homomorphism on...

Idempotent, Nilpotent, Zero divisor Characteristic (algebra) Ring homomorphism, Algebra homomorphism Ring epimorphism Ring monomorphism Ring isomorphism Skolem–Noether...

The extension C ′ {\displaystyle C'} of C {\displaystyle C} , is a homomorphism of S ∗ {\displaystyle S^{*}} into T ∗ {\displaystyle T^{*}} , which naturally...

tu(Ψ(y))(x), we find that B(x, y) = tB(y, x). Here, Ψ is the natural homomorphism X → X## into the double dual. If the vector spaces X and Y have respectively...

feature of the L 1 {\displaystyle L^{1}} Fourier transform is that it is a homomorphism of Banach algebras from L 1 {\displaystyle L^{1}} equipped with the convolution...

}(M)} . This odd derivation is defined by extending the Lie algebra homomorphism g → C ∞ ( M ) {\displaystyle {\mathfrak {g}}\to C^{\infty }(M)} of the...

ring R and a subset S, one wants to construct some ring R* and ring homomorphism from R to R*, such that the image of S consists of units (invertible...