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The chromatic invariant theta(G) of a connected graph G is the number of spanning trees of G that have internal activity 1 and external activity 0. For graphs other than the ...

An operator T which commutes with all shift operators E^a, so TE^a=E^aT for all real a in a field. Any two shift-invariant operators commute.

An integer kappa equal to 0 or 1 which vanishes iff the product manifold M^4×R can be given a smooth structure. Here, M^n is a compact connected topological four-manifold.

The quantity ps-rq obtained by letting x = pX+qY (1) y = rX+sY (2) in ax^2+2bxy+cy^2 (3) so that A = ap^2+2bpr+cr^2 (4) B = apq+b(ps+qr)+crs (5) C = aq^2+2bqs+cs^2 (6) and ...

To define a recurring digital invariant of order k, compute the sum of the kth powers of the digits of a number n. If this number n^' is equal to the original number n, then ...

Let omega_1 and omega_2 be periods of a doubly periodic function, with tau=omega_2/omega_1 the half-period ratio a number with I[tau]!=0. Then Klein's absolute invariant ...

The Hopf invariant one theorem, sometimes also called Adams' theorem, is a deep theorem in homotopy theory which states that the only n-spheres which are H-spaces are S^0, ...

Theta(G;A)=<theta(a):a in A-1> is an A-invariant solvable p^'-subgroup of G.

A subring of a ring R is a subgroup of R that is closed under multiplication.

A group L is a component of H if L is a quasisimple group which is a subnormal subgroup of H.