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The hat polykite is an aperiodic monotile discovered by Smith et al. (2023). It is illustrated above in an aperiodic tiling (Smith et al. 2023).

The polynomials in the diagonal of the Smith normal form or rational canonical form of a matrix are called its invariant factors.

Find the figure bounded by a line which has the maximum area for a given perimeter. The solution is a semicircle. The problem is based on a passage from Virgil's Aeneid: "The ...

Let Jones and Smith be the only two contestants in an election that will end in a deadlock when all votes for Jones (J) and Smith (S) are counted. What is the expectation ...

The nth k-statistic k_n is the unique symmetric unbiased estimator of the cumulant kappa_n of a given statistical distribution, i.e., k_n is defined so that <k_n>=kappa_n, ...

The set difference A\B is defined by A\B={x:x in A and x not in B}. Here, the backslash symbol is defined as Unicode U+2216. The set difference is therefore equivalent to the ...

An aperiodic monotile, also somewhat humorously known as an einstein (where "einstein" means "one stone", perhaps generalizable to "one tile," in German), is a single tile ...

The statistics h_(r,s,...) defined such that <h_(r,s,...)>=mu_rmu_s..., where mu_r is a central moment. These statistics generalize h-statistics and were originally called ...

The rth sample raw moment m_r^' of a sample with sample size n is defined as m_r^'=1/nsum_(k=1)^nx_k^r. (1) The sample raw moments are unbiased estimators of the population ...

The nth Smarandache-Wellin number is formed from the consecutive number sequence obtained by concatenating of the digits of the first n primes. The first few are 2, 23, 235, ...