The affine symmetric groups are a family of mathematical structures that
describe the symmetries of the number line and the regular triangular
tiling of the plane (pictured), as well as related higher-dimensional
objects. They may also be defined as collections of permutations
(rearrangements) of the integers that are periodic in a certain sense,
or in purely algebraic terms as a group with certain generators and
relations. They are studied in the fields of combinatorics and
representation theory. Each of these groups is an infinite extension of
a finite symmetric group, and many important combinatorial properties of
the finite symmetric groups can be extended to the corresponding affine
symmetric groups. The affine symmetric groups have close relationships
with other mathematical objects, including juggling patterns and certain
complex reflection groups. Many of their combinatorial and geometric
properties extend to the broader family of affine Coxeter groups.
Read more: <https://en.wikipedia.org/wiki/Affine_symmetric_group>
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Today's selected anniversaries:
1918:
World War I: After his platoon suffered heavy casualties during
the Meuse–Argonne offensive in France's Forest of Argonne, American
Corporal Alvin York led the 7 remaining men on an attack against a
German machine gun nest; 25 German soldiers were killed and 132
captured.
<https://en.wikipedia.org/wiki/Alvin_York>
1932:
The Indian Air Force was founded as an auxiliary air force of
the British Royal Air Force.
<https://en.wikipedia.org/wiki/Indian_Air_Force>
2016:
Yemen War: A funeral in Sanaa was hit by two consecutive
airstrikes by a Saudi-led coalition, leaving 143–155 civilians dead
and more than 525 injured.
<https://en.wikipedia.org/wiki/Sanaa_funeral_airstrike>
2019:
Anti-government protests calling for free and fair elections
began in Baku, Azerbaijan.
<https://en.wikipedia.org/wiki/2019_Baku_protests>
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Wiktionary's word of the day:
refusenik:
1. (Soviet Union, historical, slang) One of the citizens of the former
Soviet Union who was refused permission to emigrate (typically but not
exclusively a Jewish citizen denied permission to emigrate to Israel).
2. (by extension, informal) A person who refuses to do something,
usually as a protest; for example, one who refuses conscription or
vaccination. [...]
<https://en.wiktionary.org/wiki/refusenik>
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Wikiquote quote of the day:
Political extremism involves two prime ingredients: an
excessively simple diagnosis of the world's ills, and a conviction that
there are identifiable villains back of it all. Such extremism comes
easily to men who have doped themselves with delusions of their own
overriding virtue and the rascality of others.
--John W. Gardner
<https://en.wikiquote.org/wiki/John_W._Gardner>
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