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The Hadwiger conjecture is a generalization of the four-color theorem which states that for any loopless graph G with h(G) the Hadwiger number and chi(G) the chromatic ...

The Montgomery-Odlyzko law (which is a law in the sense of empirical observation instead of through mathematical proof) states that the distribution of the spacing between ...

A numeral is a symbol used to represent a number. Arabic numerals (0-9) are the ones most commonly used today. Other types, mainly of historical interest, include Egyptian, ...

The principal theorem of axonometry, first published without proof by Pohlke in 1860. It states that three segments of arbitrary length a^'x^', a^'y^', and a^'z^' which are ...

A conjecture due to M. S. Robertson in 1936 which treats a univalent power series containing only odd powers within the unit disk. This conjecture implies the Bieberbach ...

Conditions arising in the study of the Robbins axiom and its connection with Boolean algebra. Winkler studied Boolean conditions (such as idempotence or existence of a zero) ...

A diagram lemma which states that every short exact sequence of chain complexes and chain homomorphisms 0-->C-->^phiD-->^psiE-->0 gives rise to a long exact sequence in ...

If k|n, then the complete k-uniform hypergraph on n vertices decomposes into 1-factors, where a 1-factor is a set of n/k pairwise disjoint k-sets. Brouwer and Schrijver ...

A braid with M strands and R components with P positive crossings and N negative crossings satisfies |P-N|<=2U+M-R<=P+N, where U is the unknotting number. While the second ...

Let there be three polynomials a(x), b(x), and c(x) with no common factors such that a(x)+b(x)=c(x). Then the number of distinct roots of the three polynomials is one or more ...