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The problem of finding the strategy to guarantee reaching the boundary of a given region ("forest") in the shortest distance (i.e., a strategy having the best worst-case ...

Lucas's theorem states that if n>=3 be a squarefree integer and Phi_n(z) a cyclotomic polynomial, then Phi_n(z)=U_n^2(z)-(-1)^((n-1)/2)nzV_n^2(z), (1) where U_n(z) and V_n(z) ...

The Markström graph is a cubic planar graph on 24 vertices which lacks cycles of length 4 and 8 but contains cycles of length 16. (In particular, it contains cycles of ...

A Meyniel graph, also called a very strongly perfect graph, is a graph in which every odd cycle of length five or more has at least two chords. Meyniel graphs are perfect. ...

There exist lattices in n dimensions having hypersphere packing densities satisfying eta>=(zeta(n))/(2^(n-1)), where zeta(n) is the Riemann zeta function. However, the proof ...

Let A={a_1,a_2,...} be a free Abelian semigroup, where a_1 is the identity element, and let mu(n) be the Möbius function. Define mu(a_n) on the elements of the semigroup ...

Tiling of a Möbius strip can be performed immediately by carrying over a tiling of a rectangle with the same two-sided surface area. However, additional tilings are possible ...

A monotone triangle (also called a strict Gelfand pattern or a gog triangle) of order n is a number triangle with n numbers along each side and the base containing entries ...

The multinomial coefficients (n_1,n_2,...,n_k)!=((n_1+n_2+...+n_k)!)/(n_1!n_2!...n_k!) (1) are the terms in the multinomial series expansion. In other words, the number of ...

The neighborhood complex N(G) of a locally finite graph G is defined as the abstract simplicial complex formed by the subsets of the neighborhoods of all vertices of G.