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- W4300807854 abstract "An m-ballot path of size n is a path on the square grid consisting of north and east steps, starting at (0,0), ending at (mn,n), and never going below the line {x=my}. The set of these paths can be equipped with a lattice structure, called the m-Tamari lattice, which generalizes the usual Tamari lattice obtained when m=1. We prove that the number of intervals in this lattice is $$ frac {m+1}{n(mn+1)} {(m+1)^2 n+mchoose n-1}. $$ This formula was recently conjectured by Bergeron in connection with the study of coinvariant spaces. The case m=1 was proved a few years ago by Chapoton. Our proof is based on a recursive description of intervals, which translates into a functional equation satisfied by the associated generating function. The solution of this equation is an algebraic series, obtained by a guess-and-check approach. Finding a bijective proof remains an open problem." @default.
- W4300807854 created "2022-10-04" @default.
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- W4300807854 date "2011-06-08" @default.
- W4300807854 modified "2023-09-29" @default.
- W4300807854 title "The number of intervals in the m-Tamari lattices" @default.
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