4 papers
Binomial coefficients and the operadic butterfly
Vladimir Dotsenko, Medet Jumadildayev
We prove the conjecture of Laubie on dimensions of components of two operads completing Loday's operadic butterfly diagram. For one of these operads, the dimension of the -th co…
Increasing Trees and the Degree-Chromatic Polynomial
Medet Jumadildayev
This paper studies increasing trees on labeled vertices, in which labels increase from the root to the leaves. It is known that the number of binary increasing trees coincides…
Enumeration of multipartite series-reduced trees
Medet Jumadildayev
We obtain a generating function for the degree sequences and colors of rooted multipartite labeled series-reduced trees. As an application of this result, we determine the number o…
Duality Relations of Graph Polynomials
Medet Jumadildayev
The duality theorem of Lass relates the matching polynomials of a simple graph with the matching polynomials of its complement . In particular, this relation gives rise…