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Module multiplicity is a number associated with every nonzero finitely generated graded module M over a graded ring R for which the Hilbert series is defined. If dim(M)=d, ...

Perhaps the most commonly-studied oriented point lattice is the so-called north-east lattice which orients each edge of L in the direction of increasing coordinate-value. ...

A lattice L is said to be oriented if there exists a rule which assigns a specified direction to any edge connecting arbitrary lattice points x_i,x_j in L. In that way, an ...

In elementary geometry, orthogonal is the same as perpendicular. Two lines or curves are orthogonal if they are perpendicular at their point of intersection. Two vectors v ...

The principal theorem of axonometry, first published without proof by Pohlke in 1860. It states that three segments of arbitrary length a^'x^', a^'y^', and a^'z^' which are ...

A typical vector (i.e., a vector such as the radius vector r) is transformed to its negative under inversion of its coordinate axes. Such "proper" vectors are known as polar ...

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 Rees ring of R with respect to F is R_+(F)=I_0 direct sum ...

The rook numbers r_k^((m,n)) of an m×n board are the number of subsets of size k such that no two elements have the same first or second coordinate. In other word, it is the ...

The spherical harmonics Y_l^m(theta,phi) are the angular portion of the solution to Laplace's equation in spherical coordinates where azimuthal symmetry is not present. Some ...

The contraction of a tensor is obtained by setting unlike indices equal and summing according to the Einstein summation convention. Contraction reduces the tensor rank by 2. ...