Permanent

In linear algebra, the permanent of a square matrix is a function of the matrix similar to the determinant. The permanent, as well as the determinant, is a polynomial in the entries of the matrix. Both permanent and determinant are special cases of a more general function of a matrix called the immanant.

Definition

The permanent of an n-by-n matrix A = (a_i,j) is defined as

The sum here extends over all elements σ of the symmetric group S_n; i.e. over all permutations of the numbers 1, 2, ..., n.

For example,

and

The definition of the permanent of A differs from that of the determinant of A in that the signatures of the permutations are not taken into account.

The permanent of a matrix A is denoted per A, perm A, or Per A, sometimes with parentheses around the argument. In his monograph, Minc (1984) uses Per(A) for the permanent of rectangular matrices, and uses per(A) when A is a square matrix. Muir (1882) uses the notation .

The word, permanent, originated with Cauchy in 1812 as “fonctions symétriques permanentes” for a related type of function, and was used by Muir (1882) in the modern, more specific, sense.

Randonneuring

Randonneuring (also known as Audax in the UK, Australia and Brazil) is a long-distance cycling sport with its origins in audax cycling. In randonneuring, riders attempt courses of 200 km or more, passing through predetermined "controls" (checkpoints) every few tens of kilometers. Riders aim to complete the course within specified time limits, and receive equal recognition regardless of their finishing order. Riders may travel in groups or alone as they wish, and are expected to be self-sufficient between controls. A randonneuring event is called a randonnée or brevet, and a rider who has completed a 200 km event is called a randonneur. The international governing body for randonneuring is Audax Club Parisien (ACP), which works with other randonneuring organisations worldwide through Les Randonneurs Mondiaux (RM). Randonneuring is popular in France, and has a following in the Netherlands, Belgium, United Kingdom, Australia, USA, Canada, Brazil and India.

History

Karlgeorg Hoefer

Karlgeorg Hoefer (February 6, 1914 – October 8, 2000) was a German calligrapher and typographer.

Hoefer was born in Schlesisch-Drehnow (now Drzonów) in Silesia. He taught typography at the Hochschule für Gestaltung Offenbach (until 1970 "Werkkunstschule Offenbach"). He held several calligraphy workshops for calligraphic societies in Los Angeles, San Francisco, Portland, Boston, Minneapolis-St. Paul, Portland and Washington. In 1987 he founded the Schreibwerkstatt-Klingspor Offenbach and supported the Klingspor Museum in Offenbach am Main.

He designed fonts for Linotype, Klingspor, and Ludwig & Mayer.

Today his most commonly seen font is the FE-Schrift, the standard font for German number plates.

He died in Offenbach in 2000.

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