57 citations · 275 across the 73 of their papers we have counts for
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math.CO2003
Periodic de Bruijn triangles: exact and asymptotic results
B. Shapiro, M. Shapiro, A. Vainshtein
We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic for…
math.CO2003★ 1 cited
Trees, parking functions, syzygies, and deformations of monomial ideals
Alexander Postnikov, Boris Shapiro
For a graph G, we construct two algebras, whose dimensions are both equal to the number of spanning trees of G. One of these algebras is the quotient of the polynomial ring modulo…