We present algorithms for searching and generating solutions to the equation x<sub>1</sub><sup>2</sup>+x<sub>2</sub><sup>2</sup>+ ...+x<sub>n</sub><sup>2</sup> =â€¦ (More)

The authors give a history of the so-called tennis ball problem, and discuss its relation to lattice path enumeration. We also prove a conjecture related to a solution of the symmetric case, namelyâ€¦ (More)

Let (I1; I2; :::; Ik) be a random k-tuple of subintervals of the discrete interval [1; n], and Ln the random variable that measures the size of their insersection. We derive the exact and asymptoticâ€¦ (More)

The enumeration of integer-matrices has been the subject of considerable study and it is unlikely that a simple formula exists. The number in question can be related in various ways to theâ€¦ (More)

Many famous researchers in computer science, mathematics and other areas have studied enumerative problems in lattice path and walks which could be applied to many fields. We will discuss some newâ€¦ (More)

In the more than 100 years since Markoff-Hurwitz Equations, they play a decisive role, have turned up in an astounding variety of different settings, from number theory to combinatorics, fromâ€¦ (More)

In our "Unsolved Problems in Computational Science", we will talk about some interesting open problems in computational science. These problems are related to number theory, geometry theory,â€¦ (More)