As we have seen before, in order to define a partial action of a group G on a set X, we have to assign to each element g [member of] G a bijection
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] between two subsets of X such that the compositions of these bijections
, wherever they are defined, should be compatible with the group operation.
The proof is based on Corteel and Nadeau's bijection
between permutation tableaux and permutations.
This construction produces a simple bijection
from [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] to the set [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] of permutations in [F.
A connected graph G (V , E) is said to be (a, d ) -antimagic if there exist positive integers a, d and a bijection
Hollander proved that necessary conditions for Cn P2 to be (a, d ) -antimagic.
He showed that there exists an order-preserving bijection
between the set of cones in S and the set of left amenable partial orders on S.
It's easy to see that existence of [psi] requires [PSI] to be bijection
, we denote [psi] = [[PHI].
Then there is a bijection
between the set of subgroups of G/N and the set of subgroups of G which contain N such that:
If this theorem is true it would apparently make hidden variables completely redundant since it would be always possible to define a bijection
or relation of equivalence between the [lambda] space and the Hilbert space: (loosely speaking we could in principle make the correspondence [lambda] [?
They obtain explicit diagrammatical formulas for the decomposition of products of divided powers one-morphisms as direct sums of indecomposable one-morphisms, which are in a bijection
with the Lusztig canonical basis elements.
2] have shown that there is bijection
between a set of Bregman divergences and members of the regular exponential family of probability distributions.
[lambda]: Q [lambda] Q is a left-regular permutation or right-regular permutation of (Q, *), if for all x,y [member of] Q one has [lambda] (xy) = [lambda] (x) * y or [rho](xy)= x * [rho] (y), respectively.
Then it is easy to check that f is a bijection
from the vertex set of [P.