V. Retakh

activity

19942025

most citedNoncommutative symmetric functions

163 citations · 327 across the 36 of their papers we have counts for

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3 papers · 1 filter

math.CO2012★ 1 cited

The Reciprocal of $\sum_{n \geq 0} a^{n} b^{n}$ for non-commuting $a$ and $b$ , Catalan numbers and non-commutative quadratic equations

Arkady Berenstein, Vladimir Retakh, Christophe Reutenauer +1

The aim of this paper is to describe the inversion of the sum $\sum_{n \geq 0} a^{n} b^{n}$ where $a$ and $b$ are non-commuting variables as a formal series in $a$ and $b$ . We show that t…

math.CO2007

Algebras associated to acyclic directed graphs

Vladimir Retakh, Robert Lee Wilson

We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices. Each finite directed acyclic gr…

math.CO2006

Hilbert series of algebras associated to directed graphs

Vladimir Retakh, Shirlei Serconek, Robert Lee Wilson

Few changes. We compute the Hilbert series of some algebras associated to directed graphs and related to factorizations of noncommutative polynomials.

The Reciprocal of ∑n≥0​anbn for non-commuting a and b, Catalan numbers and non-commutative quadratic equations

Algebras associated to acyclic directed graphs

Hilbert series of algebras associated to directed graphs

The Reciprocal of $\sum_{n \geq 0} a^{n} b^{n}$ for non-commuting $a$ and $b$ , Catalan numbers and non-commutative quadratic equations