5 citations · 7 across the 4 of their papers we have counts for
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math.CO1999
Restricted permutations, continued fractions, and Chebyshev polynomials
T. Mansour, A. Vainshtein
Let f_n^r(k) be the number of 132-avoiding permutations on n letters that contain exactly r occurrences of 12... k, and let F_r(x;k) and F(x,y;k) be the generating functions define…
math.AG1999
Simply-laced Coxeter groups and groups generated by symplectic transvections
Boris Shapiro, Michael Shapiro, Alek Vainshtein +1
Let W be an arbitrary Coxeter group of simply-laced type (possibly infinite but of finite rank), u,v be any two elements in W, and i be a reduced word (of length m) for the pair (u…
math.AG1999
The number of ramified coverings of the sphere by the torus and surfaces of higher genera
P. P. Goulden, D. M. Jackson, A. Vainshtein
We obtain an explicit expression for the number of ramified coverings of the sphere by the torus with given ramification type for a small number of ramification points, and conject…