Séminaire Lotharingien de Combinatoire, 93B.82 (2025), 12 pp.
Samuele Giraudo and Yannic Vargas
Operads of Packed Words, Quotients, and Monomial Bases
Abstract.
The associative operad is a central structure in operad theory, defined on the linear
span of permutations. We build two analogs of the associative operad on the linear span
of packed words. By seeing a packed word as a surjective map between two finite sets,
our first operad is graded by the cardinality of the domain and the second one, by the
cardinality of the codomain. In the same way as the associative operad of permutations
admits as quotients the duplicial and interstice operads, we derive similar structures
for our operads of packed words. Both operadic operations on monomial bases, constructed
from partial orders on packed words, are monomial-positive. We propose also an analogue
of Dynkin idempotent of Zie algebras in this context of operads of packed words.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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