Combinatorics of Cyclic Shifts in Plactic, Hypoplactic, Sylvester, and Related Monoids

  • Alan J. CainEmail author
  • António Malheiro
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10432)


The cyclic shift graph of a monoid is the graph whose vertices are elements of the monoid and whose edges link elements that differ by a cyclic shift. For certain monoids connected with combinatorics, such as the plactic monoid (the monoid of Young tableaux) and the sylvester monoid (the monoid of binary search trees), connected components consist of elements that have the same evaluation (that is, contain the same number of each generating symbol). This paper discusses new results on the diameters of connected components of the cyclic shift graphs of the finite-rank analogues of these monoids, showing that the maximum diameter of a connected component is dependent only on the rank. The proof techniques are explained in the case of the sylvester monoid.


Cyclic shift Plactic monoid Sylvester monoid Binary search tree Cocharge 


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Departamento de Matemática and Centro de Matemática e Aplicações, Faculdade de Ciências e TecnologiaUniversidade Nova de LisboaCaparicaPortugal

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