Plactic, hypoplactic, and Sylvester monoids, and other homogeneous monoids
 
 
Description:  In recent work with Gray and Malheiro, I proved that finite-rank plactic monoids (in which Young tableaux form a cross-section) admit finite convergent presentations and are biautomatic. This seminar will survey three themes arising from this work:
(1) Using similar techniques with rather different tricks (sometimes exploiting connections with combinatorics) to prove that other hypoplactic monoids (in which quasi-ribbon tableaux form a cross-section) and Sylvester monoids (in which binary search trees form a cross-section) admit finite convergent presentations and are biautomatic.
(2) The relationship, within the class of homogeneous monoids, of the properties of admitting a finite convergent presentation, finite derivation type, automaticity, and biautomaticity. (Admitting a finite convergent presentation implies finite derivation type, and biautomaticity implies automaticity, but otherwise these properties are independent for general monoids.)
(3) Combinatorial characterization of conjugacy for certain homogeneous monoids, and deciding conjugacy for homogeneous monoids.
Date:  2015-02-25
Start Time:   14:30
Speaker:  Alan Cain (CMA, Univ. Nova de Lisboa)
Institution:  CMA, Univ. Nova de Lisboa
Place:  Room 5.5
Research Groups: -Algebra and Combinatorics
-Algebra, Logic and Topology
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