Geodesic
The \(m\)-colored composition poset
The electronic journal of combinatorics, Tome 14 (2007)
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We define a partial order on colored compositions with many properties analogous to Young's lattice. We show that saturated chains correspond to colored permutations, and that covering relations correspond to a Pieri-type rule for colored quasi-symmetric functions. We also show that the poset is CL-shellable. In the case of a single color, we recover the subword order on binary words.
DOI : 10.37236/941
Classification : 06A07, 52B22
Mots-clés : partial order, colored compositions, saturated chains, colored permutations, covering relations, quasi-symmetric functions, subword order 
@article{10_37236_941,
     author = {Brian Drake and T. Kyle Petersen},
     title = {The \(m\)-colored composition poset},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/941},
     zbl = {1110.06004},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/941/}
}
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Brian Drake; T. Kyle Petersen. The \(m\)-colored composition poset. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/941

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