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Two patterns T_1 and T_2 belong to the same Wilf class if |S_n(T_1)|=|S_n(T_2)| for all n, where S_n(T) denotes the set of permutations on {1,...,n} that avoid the pattern T. ...

Schur (1916) proved that no matter how the set of positive integers less than or equal to |_n!e_| (where |_x_| is the floor function) is partitioned into n classes, one class ...

An n-bridge knot is a knot with bridge number n. The set of 2-bridge knots is identical to the set of rational knots. If L is a 2-bridge knot, then the BLM/Ho polynomial Q ...

Given any open set U in R^n with compact closure K=U^_, there exist smooth functions which are identically one on U and vanish arbitrarily close to U. One way to express this ...

Let E be a simply connected compact set in the complex plane. By the Riemann mapping theorem, there is a unique analytic function ...

A chord of a graph cycle C is an edge not in the edge set of C whose endpoints lie in the vertex set C (West 2000, p. 225). For example, in the diamond graph as labeled ...

A disk algebra is an algebra of functions which are analytic on the open unit disk in C and continuous up to the boundary. A representative measure for a point x in the ...

The essential supremum is the proper generalization to measurable functions of the maximum. The technical difference is that the values of a function on a set of measure zero ...

A set of algebraic invariants for a quantic such that any invariant of the quantic is expressible as a polynomial in members of the set. Gordan (1868) proved the existence of ...

A set of generators (g_1,...,g_n) is a set of group elements such that possibly repeated application of the generators on themselves and each other is capable of producing ...