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Macdonald's constant term conjectures are related to root systems of Lie algebras (Macdonald 1982, Andrews 1986). They can be regarded as generalizations of Dyson's ...

The mean line segment length l^_ is the average length of a line segment in line segment picking within some given shape. As summarized in the following table (where Delta(3) ...

A group whose group operation is identified with multiplication. As with normal multiplication, the multiplication operation on group elements is either denoted by a raised ...

In the technical combinatorial sense, an a-ary necklace of length n is a string of n characters, each of a possible types. Rotation is ignored, in the sense that b_1b_2...b_n ...

Given a positive integer m>1, let its prime factorization be written m=p_1^(a_1)p_2^(a_2)p_3^(a_3)...p_k^(a_k). (1) Define the functions h(n) and H(n) by h(1)=1, H(1)=1, and ...

There are several sorts of graphs referred to as "star graphs" in mathematics, computer science, and information processing. The most common sort of star is the n-star graph ...

Let A be the area of a simply closed lattice polygon. Let B denote the number of lattice points on the polygon edges and I the number of points in the interior of the ...

Consider a set A_n={a_1,a_2,...,a_n} of n positive integer-denomination postage stamps sorted such that 1=a_1<a_2<...<a_n. Suppose they are to be used on an envelope with ...

A primality test that provides an efficient probabilistic algorithm for determining if a given number is prime. It is based on the properties of strong pseudoprimes. The ...

The Robertson graph is the unique (4,5)-cage graph, illustrated above. It has 19 vertices and 38 edges. It has girth 5, diameter 3, chromatic number 3, and is a quartic ...