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math.CO2007★ 1 cited
The number of lattice paths below a cyclically shifting boundary
J. Irving, A. Rattan
We count the number of lattice paths lying under a cyclically shifting piecewise linear boundary of varying slope. Our main result extends well known enumerative formulae concernin…
math.CO2005
An explicit form for Kerov's character polynomials
I. P. Goulden, A. Rattan
Kerov considered the normalized characters of irreducible representations of the symmetric group, evaluated on a cycle, as a polynomial in free cumulants. Biane has proved that thi…