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The associahedron is the n-dimensional generalization of the pentagon. It was discovered by Stasheff in 1963 and it is also known as the Stasheff polytope. The number of ...

Given a module M over a commutative unit ring R and a filtration F:... subset= I_2 subset= I_1 subset= I_0=R (1) of ideals of R, the associated graded module of M with ...

Given a commutative unit ring R and a filtration F:... subset= I_2 subset= I_1 subset= I_0=R (1) of ideals of R, the associated graded ring of R with respect to F is the ...

Given a principal bundle pi:A->M, with fiber a Lie group G and base manifold M, and a group representation of G, say phi:G×V->V, then the associated vector bundle is ...

Let phi:M->M be a C^1 diffeomorphism on a compact Riemannian manifold M. Then phi satisfies Axiom A if the nonwandering set Omega(phi) of phi is hyperbolic and the periodic ...

Propositional calculus, first-order logic, and other theories in mathematical logic are defined by their axioms (or axiom schemata, plural: axiom schemata) and inference ...

The axiom of Zermelo-Fraenkel set theory which asserts that sets formed by the same elements are equal, forall x(x in a=x in b)=>a=b. Note that some texts (e.g., Devlin ...

The axiom of Zermelo-Fraenkel set theory which asserts the existence for any set a and a formula A(y) of a set x consisting of all elements of a satisfying A(y), exists x ...

An Aztec diamond of order n is the region obtained from four staircase shapes of height n by gluing them together along the straight edges. It can therefore be defined as the ...

Let P(x) be defined as the power series whose nth term has a coefficient equal to the nth prime p_n, P(x) = 1+sum_(k=1)^(infty)p_kx^k (1) = 1+2x+3x^2+5x^3+7x^4+11x^5+.... (2) ...