Related papers: Unprovability results involving braids
We describe new types of normal forms for braid monoids, Artin-Tits monoids, and, more generally, for all monoids in which divisibility has some convenient lattice properties (``locally Garside monoids''). We show that, in the case of…
We give a simple characterization of braids that can be unplaited keeping separately their upper ends and their lower ends tied together
In a previous work [11], the author considered a representation of the braid group \rho: B_n\to GL_m(\Bbb Z[q^{\pm 1},t^{\pm 1}]) (m=n(n-1)/2), and proved it to be faithful for n=4. Bigelow [3] then proved the same representation to be…
Given a category with a bifunctor and natural isomorphisms for associativity, commutativity and left and right identity we do not assume that extra constraining diagrams hold. We introduce groupoids of coupling trees to describe a version…
In this note we present a characterisation of all unary and binary patterns that do not only contain variables, but also reversals of their instances. These types of variables were studied recently in either more general or particular…
In introductory books about natural numbers, a common kind of assertion - often left as exercise to the reader - is that certain forms of induction on $\mathbb{N}$ (regular/ordinary, complete/strong) are equivalent one to each other and to…
Presentations for unbraided, braided and symmetric pseudomonoids are defined. Biequivalences characterising the semistrict bicategories generated by these presentations are proven. It is shown that these biequivalences categorify results in…
Random braids that are formed by multiplying randomly chosen permutation braids are studied by analyzing their behavior under Garside's weighted decomposition and cycling. Using this analysis, we propose a polynomial-time algorithm to the…
We describe symmetries of the braid monodromy decomposition for a class of plane curves defined over reals including the real curves with no real points and proving new divisibility relations for Alexander invariants of such curves.
We define invariants of braids rather than invariants of conjugacy classes of braids. For any pure three-braid we give effective upper and lower bounds for these invariants. This is done in terms of a natural syllable decomposition of the…
We introduce the notion of unavoidable (complete) sets of word patterns, which is a refinement for that of words, and study certain numerical characteristics for unavoidable sets of patterns. In some cases we employ the graph of pattern…
We consider first-order logics of sequences ordered by the subsequence ordering, aka sequence embedding. We show that the \Sigma_2 theory is undecidable, answering a question left open by Kuske. Regarding fragments with a bounded number of…
We investigate relationships between versions of derivability conditions for provability predicates. We show several implications and non-implications between the conditions, and we discuss unprovability of consistency statements induced by…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
We give two general constructions of braid equivalences which exist between certain deformations of the 2-branched Horsehoe map. We then give numerical evidence suggesting that these constructions of braid equivalences are always realised…
We show that there is a family of pseudo-Anosov braids independently parameterized by the braid index and the (canonical) length whose smallest conjugacy invariant sets grow exponentially in the braid index and linearly in the length and…
Contrary to the expected behavior, we show the existence of non-invertible deformations of Lie algebras which can generate invariants for the coadjoint representation, as well as delete cohomology with values in the trivial or adjoint…
We consider Proof Complexity in light of the unusual binary encoding of certain combinatorial principles. We contrast this Proof Complexity with the normal unary encoding in several refutation systems, based on Resolution and Integer Linear…
We prove a general divisibility theorem that implies, e.g., that, in any group, the number of generating pairs (as well as triples, etc.) is a multiple of the order of the commutator subgroup. Another corollary says that, in any associative…
We present a method to prove the decidability of provability in several well-known inference systems. This method generalizes both cut-elimination and the construction of an automaton recognizing the provable propositions.