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The dimension of a partially ordered set P=(X,<=) is the size of the smallest realizer of P. Equivalently, it is the smallest integer d such that P is isomorphic to a ...

A knot obtained from a tangle which can be represented by a finite sequence of integers.

Let R be a commutative ring. A category C is called an R-category if the Hom-sets of C are R-modules.

Let H be a subgroup of G. A subset T of elements of G is called a right transversal of H if T contains exactly one element of each right coset of H.

A graph G whose line graph is L(G) is called the root graph R(L(G)) of L(G). In order words, R(L(G))=G. The root graph of a connected graph is unique except for K_3=C_3 (the ...

An n-route is defined as a walk of length n with specified initial point in which no line succeeds itself.

A functor which defines an equivalence of module categories.

Eliminate each knot crossing by connecting each of the strands coming into the crossing to the adjacent strand leaving the crossing. The resulting strands no longer cross but ...

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).