95 citations · 300 across the 23 of their papers we have counts for
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math.CO2011★ 28 cited
Shuffle algebras, homology, and consecutive pattern avoidance
Vladimir Dotsenko, Anton Khoroshkin
Shuffle algebras are monoids for an unconvential monoidal category structure on graded vector spaces. We present two homological results on shuffle algebras with monomial relations…
math.CO2010★ 2 cited
Using homological duality in consecutive pattern avoidance
Anton Khoroshkin, Boris Shapiro
Using the approach suggested in [arXiv:1002.2761] we present below a sufficient condition guaranteeing that two collections of patterns of permutations have the same exponential ge…
math.CO2010★ 11 cited
Anick-type resolutions and consecutive pattern avoidance
Vladimir Dotsenko, Anton Khoroshkin
For permutations avoiding consecutive patterns from a given set, we present a combinatorial formula for the multiplicative inverse of the corresponding exponential generating funct…