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There are several versions of the Kaplan-Yorke conjecture, with many of the higher dimensional ones remaining unsettled. The original Kaplan-Yorke conjecture (Kaplan and ...

A theorem giving a criterion for an origami construction to be flat. Kawasaki's theorem states that a given crease pattern can be folded to a flat origami iff all the ...

Let G be a planar graph whose vertices have been properly colored and suppose v in V(G) is colored C_1. Define the C_1C_2-Kempe chain containing v to be the maximal connected ...

C. Kimberling has extensively tabulated and enumerated the properties of triangle centers (Kimberling 1994, 1998, and online), denoting the nth center in his numbering scheme ...

The 60 Pascal lines of a hexagon inscribed in a conic intersect three at a time through 20 Steiner points, and also three at a time in 60 points known as Kirkman points. Each ...

A Kirkman triple system of order v=6n+3 is a Steiner triple system with parallelism (Ball and Coxeter 1987), i.e., one with the following additional stipulation: the set of ...

Klee's identity is the binomial sum sum_(k=0)^n(-1)^k(n; k)(n+k; m)=(-1)^n(n; m-n), where (n; k) is a binomial coefficient. For m=0, 1, ... and n=0, 1,..., the following ...

Kloosterman's sum is defined by S(u,v,n)=sum_(h)exp[(2pii(uh+vh^_))/n], (1) where h runs through a complete set of residues relatively prime to n and h^_ is defined by hh^_=1 ...

A combinatorial conjecture formulated by Kneser (1955). It states that whenever the n-subsets of a (2n+k)-set are divided into k+1 classes, then two disjoint subsets end up ...

The problem of determining how many nonattacking knights K(n) can be placed on an n×n chessboard. For n=8, the solution is 32 (illustrated above). In general, the solutions ...