Geodesic
A combinatorial representation with Schröder paths of biorthogonality of Laurent biorthogonal polynomials
The electronic journal of combinatorics, Tome 14 (2007)
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Combinatorial representation in terms of Schröder paths and other weighted plane paths are given of Laurent biorthogonal polynomials (LBPs) and a linear functional with which LBPs have orthogonality and biorthogonality. Particularly, it is clarified that quantities to which LBPs are mapped by the corresponding linear functional can be evaluated by enumerating certain kinds of Schröder paths, which imply orthogonality and biorthogonality of LBPs.
DOI : 10.37236/955
Classification : 05A15, 42C05, 33C45 
@article{10_37236_955,
     author = {Shuhei Kamioka},
     title = {A combinatorial representation with {Schr\"oder} paths of biorthogonality of {Laurent} biorthogonal polynomials},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/955},
     zbl = {1123.05008},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/955/}
}
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Shuhei Kamioka. A combinatorial representation with Schröder paths of biorthogonality of Laurent biorthogonal polynomials. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/955

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