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_8phi_7[a,qa^(1/2),-qa^(1/2),b,c,d,e,q^(-N); a^(1/2),-a^(1/2),(aq)/b,(aq)/c,(aq)/d,(aq)/e,aq^(N+1);q,(aq^(N+2))/(bcde)] ...

The (lower) domination number gamma(G) of a graph G is the minimum size of a dominating set of vertices in G, i.e., the size of a minimum dominating set. This is equivalent ...

Elder's theorem is a generalization of Stanley's theorem which states that the total number of occurrences of an integer k among all unordered partitions of n is equal to the ...

An error-correcting code is an algorithm for expressing a sequence of numbers such that any errors which are introduced can be detected and corrected (within certain ...

A one-person game played on a rectangular lattice of lamps which can be turned on and off. A move consists of flipping a "switch" inside one of the squares, thereby toggling ...

Consider the process of taking a number, adding its digits, then adding the digits of the number derived from it, etc., until the remaining number has only one digit. The ...

Rule 30 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

A scalene triangle is a triangle that has three unequal sides, such as those illustrated above.

The (upper) vertex independence number of a graph, often called simply "the" independence number, is the cardinality of the largest independent vertex set, i.e., the size of ...

A modulo multiplication group is a finite group M_m of residue classes prime to m under multiplication mod m. M_m is Abelian of group order phi(m), where phi(m) is the ...