Finally we give a couple examples to illustrate these ideas. First we use Proposition 8 to show that the connected sum of n copies of +3-surgery on the right-handed trefoil, #nS33(T2,3), for any n>0, does not bound a negative definite 4-manifold wit…

In this section we deal with the second family of Lemma 1.6. We start by discussing an example in full detail, then we proceed with the necessary computations for the whole family. The main goal of this section is to prove Proposition LABEL:secondfa…

We have introduced several FOL axiom systems GenReln for general relativity and showed that they are complete with respect to Lorentzian manifolds having the corresponding smoothness properties, see Theorem 7.2. From [3], we recalled our FOL definit…

Given a real enumerative problem ideally we would like to calculate the following data:

We studied the hybrid Babai–Černý problem, where the question is to find tight bounds on the reset threshold for automata with the full transition monoid. We presented a series of n-state automata \mathrsfsVn in this class with the reset threshold e…

Let (A,∂) be a differential graded algebra with coefficients in a noncommutative algebra A over a commutative ring R. We further assume that A=TA(M) is a tensor algebra over a free A–A-bimodule M with a preferred basis {c1,…,ck}.

The analysis of this section has been an inspiration for some later works regarding counting manifolds, which have already been published [48, 28].

Up to permutations of degree sequences and vertices, there are 14 tree degree sequence quartets on at most 10 vertices without common leaves. This appendix gives an example realization for all of them.

This research is supported under the Royal Society International Exchanges Scheme (ref. IE110369). Németi’s research was supported by OTKA grant No 81188. This work was partially undertaken whilst Stannett was a visiting fellow at the Isaac Newton I…