Search Results for ""

A convex polyomino containing at least one edge of its minimal bounding rectangle. The perimeter and area generating function for directed polygons of width m, height n, and ...

A lattice polygon formed by a three-choice walk. The anisotropic perimeter and area generating function G(x,y,q)=sum_(m>=1)sum_(n>=1)sum_(a>=a)C(m,n,a)x^my^nq^a, where ...

The log-series distribution, also sometimes called the logarithmic distribution (although this work reserves that term for a distinct distribution), is the distribution of ...

A stack polyomino is a self-avoiding convex polyomino containing two adjacent corners of its minimal bounding rectangle. The number of stack polyominoes with perimeter 2n+4 ...

If Y_i have normal independent distributions with mean 0 and variance 1, then chi^2=sum_(i=1)^rY_i^2 (1) is distributed as chi^2 with r degrees of freedom. This makes a chi^2 ...

The chi distribution with n degrees of freedom is the distribution followed by the square root of a chi-squared random variable. For n=1, the chi distribution is a ...

The first isodynamic point S has triangle center function alpha_(15)=sin(A+1/3pi) and is Kimberling center X_(15) (Kimberling 1998, p. 68).

Given a unit line segment [0,1], pick two points at random on it. Call the first point x_1 and the second point x_2. Find the distribution of distances d between points. The ...

Let a>|b|, and write h(theta)=(acostheta+b)/(2sintheta). (1) Then define P_n(x;a,b) by the generating function f(x,w)=f(costheta,w)=sum_(n=0)^inftyP_n(x;a,b)w^n ...

The theta series of a lattice is the generating function for the number of vectors with norm n in the lattice. Theta series for a number of lattices are implemented in the ...