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The Motzkin numbers enumerate various combinatorial objects. Donaghey and Shapiro (1977) give 14 different manifestations of these numbers. In particular, they give the ...

An 8-polyiamond.

The map x^' = x+1 (1) y^' = 2x+y+1, (2) which leaves the parabola x^('2)-y^'=(x+1)^2-(2x+y+1)=x^2-y (3) invariant.

The symbol v variously means "disjunction" (i.e., OR in logic) or "join" (for a lattice).

Clean tile is a game investigated by Buffon (1777) in which players bet on the number of different tiles a thrown coin will partially cover on a floor that is regularly ...

An AB percolation is a discrete percolation model in which the underlying point lattice graph L has the properties that each of its graph vertices is occupied by an atom ...

The law appearing in the definition of Boolean algebras and lattice which states that a ^ (a v b)=a v (a ^ b)=a for binary operators v and ^ (which most commonly are logical ...

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 ...

An Aztec diamond of order n is the region obtained from four staircase shapes of height n by gluing them together along the straight edges. It can therefore be defined as the ...

An equation for a lattice sum b_3(1) (Borwein and Bailey 2003, p. 26) b_3(1) = sum^'_(i,j,k=-infty)^infty((-1)^(i+j+k))/(sqrt(i^2+j^2+k^2)) (1) = ...