7 citations · 18 across the 6 of their papers we have counts for
6 papers
Non-crossing trees, quadrangular dissections, ternary trees, and duality preserving bijections
Nikos Apostolakis
Using the theory of Properly Embedded Graphs developed in an earlier work we define an involutory duality on the set labeled non-crossing trees that lifts the obvious duality in th…
A duality for labeled graphs and factorizations with applications to graph embeddings and Hurwitz enumeration
Nikos Apostolakis
The set of factorizations of permutations in to transpositions of some symmetric group is naturally in bijection with the set of graphs of order and size $m…
Lefschetz fibrations over the disc
Nikos Apostolakis, Riccardo Piergallini, Daniele Zuddas
We provide a complete set of moves relating any two Lefschetz fibrations over the disk having as their total space the same 4-dimensional 2-handlebody up to 2-equivalence. As a con…
Kauffman state sums and bracket deformation
Nikos Apostolakis, Uwe Kaiser
We derive a formula expanding the bracket with respect to a natural deformation parameter. The expansion is in terms of a two-variable polynomial algebra of diagram resolutions gen…
On 4-fold covering moves
Nikos Apostolakis
We prove the existence of a finite set of moves sufficient to relate any two representations of the same 3-manifold as a 4-fold simple branched covering of S^3. We also prove a sta…
On moves between branched coverings of S^3: The case of four sheets
Nikos Apostolakis
A combinatorial presentation of closed orientable 3-manifolds as bi-tricolored links is given together with two versions of a calculus via moves to manipulate bi-tricolored links w…