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An operator T which commutes with all shift operators E^a, so TE^a=E^aT for all real a in a field. Any two shift-invariant operators commute.

An operator E such that E^ap(x)=p(x+a).

A Skolem sequence of order n is a sequence S={s_1,s_2,...,s_(2n)} of 2n integers such that 1. For every k in {1,2,...,n}, there exist exactly two elements s_i,s_j in S such ...

sum_(k=-infty)^infty(a; m-k)(b; n-k)(a+b+k; k)=(a+n; m)(b+m; n).

A transversal design TD_lambda(k,n) of order n, block size k, and index lambda is a triple (V, G, B) such that 1. V is a set of kn elements, 2. G is a partition of V into k ...

The term "twisted sphere" is used to mean either a projective plane (Henle 1994, p. 110) or the corkscrew surface obtained by extending a sphere along a diameter and then ...

An operator T which maps some basic polynomial sequence p_n(x) into another basic polynomial sequence q_n(x).

The operator e^(nut^2/2) which satisfies e^(nut^2/2)p(x)=1/(sqrt(2pinu))int_(-infty)^inftye^(-u^2/(2nu))p(x+u)du for nu>0.

A t-(v,k,lambda) block design (abbreviated t-design) is an incidence structure of points and blocks such that the following hold: 1. There are v points, 2. Each block ...

Borsuk conjectured that it is possible to cut an n-dimensional shape of generalized diameter 1 into n+1 pieces each with diameter smaller than the original. It is true for ...