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We mainly introduce an abstract pattern to study cluster algebras. Clusteralgebras, generalized cluster algebras and Laurent phenomenon algebras areunified in the language of generalized Laurent phenomenon algebras (briefly,GLP algebras) from the perspective of Laurent phenomenon.  In this general framework, we firstly prove that each positive andd-vector-positive GLP algebra has the proper Laurent monomial property and thusits cluster monomials are linearly independent. Skew-symmetric cluster algebrasare verified to be d-vector-positive, which gives the affirmation of Conjecture[conjd] in [FZ3] in this case. And since the positivity of skew-symmetriccluster algebras is well-known, the new proof is obtained for the linearlyindependence of cluster monomials of skew-symmetric cluster algebras.  For a class of GLP algebras which are pointed, g-vectors of cluster monomialsare defined. We verify that for any positive GLP algebra pointed at $t_0$, theg-vectors ${\bf g}_{1;t}^{t_0},\cdots, {\bf g}_{n;t}^{t_0}$ form a $\mathbbZ$-basis of $\mathbb Z^n$, and different cluster monomials have differentg-vectors. As a direct application, we verify that Conjecture [conjg] in [FZ3]holds for skew-symmetrizable cluster algebras and acyclic sign-skew-symmetriccluster algebras.

Study on cluster algebras via abstract pattern and two conjectures on d-vectors and g-vector