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A snake is an Eulerian path in the d-hypercube that has no chords (i.e., any hypercube edge joining snake vertices is a snake edge). Klee (1970) asked for the maximum length ...

A solitary number is a number which does not have any friends. Solitary numbers include all primes, prime powers, and numbers for which (n,sigma(n))=1, where (a,b) is the ...

A list of five properties of a topological space X expressing how rich the "population" of open sets is. More precisely, each of them tells us how tightly a closed subset can ...

There are two types of bordism groups: bordism groups, also called cobordism groups or cobordism rings, and there are singular bordism groups. The bordism groups give a ...

The McLaughlin graph is a 112-regular graph on 275 nodes and 15400 edges that can be constructed from the Witt design. It is distance-regular with intersection array ...

Given a pick-7 lottery with 23 numbers that pays a prize to anyone matching at least 4 of the 7 numbers, there is a set of 253 tickets that guarantees a win. This set ...

A forgetful functor (also called underlying functor) is defined from a category of algebraic gadgets (groups, Abelian groups, modules, rings, vector spaces, etc.) to the ...

The Cantor set T_infty, sometimes also called the Cantor comb or no middle third set (Cullen 1968, pp. 78-81), is given by taking the interval [0,1] (set T_0), removing the ...

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. ...

A hyperbolic paraboloid is the quadratic and doubly ruled surface given by the Cartesian equation z=(y^2)/(b^2)-(x^2)/(a^2) (1) (left figure). An alternative form is z=xy (2) ...