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A column-convex polyomino is a self-avoiding convex polyomino such that the intersection of any vertical line with the polyomino has at most two connected components. ...

Exterior algebra is the algebra of the wedge product, also called an alternating algebra or Grassmann algebra. The study of exterior algebra is also called Ausdehnungslehre ...

A rational number is a number that can be expressed as a fraction p/q where p and q are integers and q!=0. A rational number p/q is said to have numerator p and denominator ...

A set of 15 open problems on Schrödinger operators proposed by mathematical physicist Barry Simon (2000). This set of problems follows up a 1984 list of open problems in ...

The problem of finding the mean triangle area of a triangle with vertices picked inside a triangle with unit area was proposed by Watson (1865) and solved by Sylvester. It ...

The Young tableau (plural, "tableaux") of a Ferrers diagram is obtained by placing the numbers 1, ..., n in the n boxes of the diagram. A "standard" Young tableau is a Young ...

Find a way to stack a square of cannonballs laid out on the ground into a square pyramid (i.e., find a square number which is also square pyramidal). This corresponds to ...

Let a_(n+1) = 1/2(a_n+b_n) (1) b_(n+1) = (2a_nb_n)/(a_n+b_n). (2) Then A(a_0,b_0)=lim_(n->infty)a_n=lim_(n->infty)b_n=sqrt(a_0b_0), (3) which is just the geometric mean.

Let g(x)=(1-x^2)(1-k^2x^2). Then int_0^a(dx)/(sqrt(g(x)))+int_0^b(dx)/(sqrt(g(x)))=int_0^c(dx)/(sqrt(g(x))), where c=(bsqrt(g(a))+asqrt(g(b)))/(sqrt(1-k^2a^2b^2)).

A nonlinear deconvolution technique used in deconvolving images from the Hubble Space Telescope before corrective optics were installed.