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Let Pi be a permutation of n elements, and let alpha_i be the number of permutation cycles of length i in this permutation. Picking Pi at random, it turns out that ...

The volume of a solid body is the amount of "space" it occupies. Volume has units of length cubed (i.e., cm^3, m^3, in^3, etc.) For example, the volume of a box (cuboid) of ...

An algorithm for finding integer relations whose running time is bounded by a polynomial in the number of real variables (Ferguson and Bailey 1992). Unfortunately, it is ...

Given a short exact sequence of modules 0->A->B->C->0, (1) let ...->P_2->^(d_2)P_1->^(d_1)P_0->^(d_0)A->0 (2) ...->Q_2->^(f_2)Q_1->^(f_1)Q_0->^(f_0)C->0 (3) be projective ...

There are several conflicting meanings associated with the notation lgx. In German and Russian literature, the notation lgx is used to mean the common logarithm log_(10)x. ...

In number theory (e.g., Ivić 2003), the symbol log_kx is commonly used to mean the nested logarithm (also called the repeated logarithm or iterated logarithm) ...

Let H be a subgroup of a group G. The similarity transformation of H by a fixed element x in G not in H always gives a subgroup. If xHx^(-1)=H for every element x in G, then ...

The term "product" refers to the result of one or more multiplications. For example, the mathematical statement a×b=c would be read "a times b equals c," where a is called ...

The square gyrobicupola is a convex equilateral solid that is Johnson solid J_(29). The unit square gyrobicupola has volume V=2+4/3sqrt(2) (1) and Dehn invariant D = 24<3>_2 ...

A power is an exponent to which a given quantity is raised. The expression x^a is therefore known as "x to the ath power." A number of powers of x are plotted above (cf. ...