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The Rogers-Selberg identities are a set of three analytic q-series identities of Rogers-Ramanujan-type appearing as equation 33, 32, and 31 in Slater (1952), A(q) = ...

Given two positive integers n and k, the bipartite Kneser graph H(n,k) is the graph whose two bipartite sets of vertices represent the k-subsets and (n-k)-subsets of ...

The Dirac matrices are a class of 4×4 matrices which arise in quantum electrodynamics. There are a variety of different symbols used, and Dirac matrices are also known as ...

The first Göllnitz-Gordon identity states that the number of partitions of n in which the minimal difference between parts is at least 2, and at least 4 between even parts, ...

A polyomino tiling is a tiling of the plane by specified types of polyominoes. Tiling by polyominoes has been investigated since at least the late 1950s, particularly by S. ...

The Schur number S(k) is the largest integer n for which the interval [1,n] can be partitioned into k sum-free sets (Fredricksen and Sweet 2000). S(k) is guaranteed to exist ...

Two lattice points (x,y) and (x^',y^') are mutually visible if the line segment joining them contains no further lattice points. This corresponds to the requirement that ...

"Analysis of Variance." A statistical test for heterogeneity of means by analysis of group variances. ANOVA is implemented as ANOVA[data] in the Wolfram Language package ...

If C_1, C_2, ...C_r are sets of positive integers and union _(i=1)^rC_i=Z^+, then some C_i contains arbitrarily long arithmetic progressions. The conjecture was proved by van ...

Let A and B_j be sets. Conditional probability requires that P(A intersection B_j)=P(A)P(B_j|A), (1) where intersection denotes intersection ("and"), and also that P(A ...