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One of the seven 4-polyhexes. S. Kim has observed that four worms solve the puzzle of finding a non-three-colorable map with only four congruent countries (as long as no ...

The Wormald graph is a unit-distance 4-chromatic graph with girth 5 on 13+5(13; 5)=6448 vertices.

The zenith angle is an angle measured from the z-axis in spherical coordinates, denoted phi in this work. It is also known as the polar angle and colatitude.

A generic word for a very large number. The term has no well-defined mathematical meaning. Conway and Guy (1996) define the nth zillion as 10^(3n+3) in the American system ...

A problem posed by the Slovak mathematician Stefan Znám in 1972 asking whether, for all integers k>=2, there exist k integers x_1,...,x_k all greater than 1 such that x_i is ...

Algebra

An acyclic digraph is a directed graph containing no directed cycles, also known as a directed acyclic graph or a "DAG." Every finite acyclic digraph has at least one node of ...

Let B_k be the kth Bernoulli number and consider nB_(n-1)=-1 (mod n), where the residues of fractions are taken in the usual way so as to yield integers, for which the ...

The conjecture that the number of alternating sign matrices "bordered" by +1s A_n is explicitly given by the formula A_n=product_(j=0)^(n-1)((3j+1)!)/((n+j)!). This ...

Andrica's conjecture states that, for p_n the nth prime number, the inequality A_n=sqrt(p_(n+1))-sqrt(p_n)<1 holds, where the discrete function A_n is plotted above. The ...