arXiv subjects
Publications and source records attributed to Paul K. Stockmeyer.
Based on known methods for computing the number of distinct score sequences for $n$-vertex tournaments, we develop algorithms for computing the number of distinct score sequences for self-complementary tournaments, strong tournaments, and tournaments that are both self-complementary and strong.
Continuing the program begun in the first paper of this series, we present a pair of non-reconstructable tournament on $p$ vertices for each $p=2^n \ge 4$.
Sequence A000975 in the Online Encyclopedia of Integer Sequences (OEIS) starts out 1, 2, 5, 10, 21, 42, 85, ... . As of July 1, 2016, the description in the OEIS lists several characterizations of this sequence and numerous examples of instances where this sequence occurs. It also presents a "not yet proved" result, a conjecture, and an unanswered question concerning this sequence. In this paper we show that all of these proposed results are in fact true.
The Pascal rhombus is a variant of Pascal's triangle in which each term is a sum of four earlier terms. Klostermeyer et al. made four conjectures about the Pascal rhombus modulo 2. In this paper we show how exploration of the stealth shape leads to unified proofs of all of these conjectures.