arXiv subjects

Frank Ruskey

Publications and source records attributed to Frank Ruskey.

21 records · Page 2Linked to original sources

arXiv2005

Which n-Venn diagrams can be drawn with convex k-gons?

We establish a new lower bound for the number of sides required for the component curves of simple Venn diagrams made from polygons. Specifically, for any n-Venn diagram of convex k-gons, we prove that k >= (2^n - 2 - n) / (n (n-2)). In the process we prove that Venn diagrams of seven curves, simple or not, cannot be formed from triangles. We then give an example achieving the new lower bound of a (simple, symmetric) Venn diagram of seven quadrilaterals. Previously Grunbaum had constructed a 7-Venn diagram of non-convex 5-gons [``Venn Diagrams II'', Geombinatorics 2:25-31, 1992].

cs.CG↗

arXiv2005

Meta-Fibonacci Sequences, Binary Trees, and Extremal Compact Codes

We look at a family of meta-Fibonacci sequences which arise in studying the number of leaves at the largest level in certain infinite sequences of binary trees, restricted compositions of an integer, and binary compact codes. For this family of meta-Fibonacci sequences and two families of related sequences we derive ordinary generating functions and recurrence relations. Included in these families of sequences are several well-known sequences in the Online Encyclopedia of Integer Sequences (OEIS).

math.CO↗

arXiv2004

Efficient coroutine generation of constrained Gray sequences

We study an interesting family of cooperating coroutines, which is able to generate all patterns of bits that satisfy certain fairly general ordering constraints, changing only one bit at a time. (More precisely, the directed graph of constraints is required to be cycle-free when it is regarded as an undirected graph.) If the coroutines are implemented carefully, they yield an algorithm that needs only a bounded amount of computation per bit change, thereby solving an open problem in the field of combinatorial pattern generation.

cs.DS↗