Deciding conjugacy in sylvester monoids and other homogeneous monoids

Abstract

We give a combinatorial characterization of conjugacy in the sylvester monoid (the monoid of binary search trees), showing that conjugacy is decidable for this monoid. We then prove that conjugacy is undecidable in general for homogeneous monoids and even for multihomogeneous monoids.

16 pages, 4 figures. Minor revisions and improvements

References in corpus (1)

• Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids

Cited by in corpus (1)

• Crystal monoids \& crystal bases: rewriting systems and biautomatic structures for plactic monoids of types $A_n$, $B_n$, $C_n$, $D_n$, and $G_2$