English

Counting the Palstars

Combinatorics 2014-06-13 v2 Discrete Mathematics Formal Languages and Automata Theory

Abstract

A palstar (after Knuth, Morris, and Pratt) is a concatenation of even-length palindromes. We show that, asymptotically, there are Θ(αkn)\Theta(\alpha_k^n) palstars of length 2n2n over a kk-letter alphabet, where αk\alpha_k is a constant such that 2k1<αk<2k122k-1 < \alpha_k < 2k-{1 \over 2}. In particular, α23.33513193\alpha_2 \doteq 3.33513193.

Keywords

Cite

@article{arxiv.1311.2318,
  title  = {Counting the Palstars},
  author = {L. Bruce Richmond and Jeffrey Shallit},
  journal= {arXiv preprint arXiv:1311.2318},
  year   = {2014}
}
R2 v1 2026-06-22T02:04:38.256Z