Journal of Integer Sequences, Vol. 25 (2022), Article 22.8.8

Nesting Nonpartitions

Joshua Marsh and Nathan Williams
Department of Mathematical Sciences
800 W. Campbell Road
Richardson, TX 75080


Antichains of root posets associated with simple complex Lie algebras are a well-studied combinatorial object, famously counted by the Coxeter-Catalan numbers. In this paper, we study chains in root posets using standard enumerative techniques. The factorizations of the zeta polynomials of these root posets gives rise to sequences that have similar numerological properties as the exponents of the Weyl group.

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(Concerned with sequences A000108 A000984 A006012 A051924.)

Received August 11 2022; revised version received October 10 2022. Published in Journal of Integer Sequences, October 26 2022.

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