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The Rogers-Selberg identities are a set of three analytic q-series identities of Rogers-Ramanujan-type appearing as equation 33, 32, and 31 in Slater (1952), A(q) = ...

The Beatty sequence is a spectrum sequence with an irrational base. In other words, the Beatty sequence corresponding to an irrational number theta is given by |_theta_|, ...

The rank polynomial R(x,y) of a general graph G is the function defined by R(x,y)=sum_(S subset= E(G))x^(r(S))y^(s(S)), (1) where the sum is taken over all subgraphs (i.e., ...

Let a closed surface have genus g. Then the polyhedral formula generalizes to the Poincaré formula chi(g)=V-E+F, (1) where chi(g)=2-2g (2) is the Euler characteristic, ...

Calculus of variations can be used to find the curve from a point (x_1,y_1) to a point (x_2,y_2) which, when revolved around the x-axis, yields a surface of smallest surface ...

The natural logarithm of 2 is a transcendental quantity that arises often in decay problems, especially when half-lives are being converted to decay constants. ln2 has ...

The q-analog of the Pochhammer symbol defined by (a;q)_k={product_(j=0)^(k-1)(1-aq^j) if k>0; 1 if k=0; product_(j=1)^(|k|)(1-aq^(-j))^(-1) if k<0; ...

The trefoil knot 3_1, also called the threefoil knot or overhand knot, is the unique prime knot with three crossings. It is a (3, 2)-torus knot and has braid word sigma_1^3. ...

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 ...

A 1-variable unoriented knot polynomial Q(x). It satisfies Q_(unknot)=1 (1) and the skein relationship Q_(L_+)+Q_(L_-)=x(Q_(L_0)+Q_(L_infty)). (2) It also satisfies ...