It is well-known that gauging a finite 0-form symmetry in quantum field theory leads to dual generated by topological Wilson line defects. These are described the representations of group which form 1-category. We argue for d-dimensional full set symmetries one obtains fact much larger and (d-1)-category, formed out lower-dimensional theories with same symmetry. study detail 2-categorical piece...

In normal version of combinatorial game theory, all games are invertible, whereas only the empty game is invertible in misère version. For this reason, several restricted universes were earlier considered for their study, in which more games are invertible. We here study combinatorial games in misère version, in particular universes where no player would like to pass their turn In these univers...

The invertible deoxyribonucleic acid (DNA) segment cloned from Salmonella sp. was radioactively labeled and used as a probe to search for homologous sequences by Southern hybridization. Only one copy of the invertible segment could be found on the Salmonella sp. genome. Partial sequence homology with the invertible region was detected in bacteriophage Mu and P1 DNA by low-stringency hybridizati...

For operators of many different kinds it has been proved that (generalized) Darboux transformations can be built using so called Wronskian formulae. Such Darboux transformations are not invertible in the sense that the corresponding mappings of the operator kernels are not invertible. The only known invertible ones were Laplace transformations (and their compositions), which are special cases o...

Mennicke–Newman lemma for unimodular rows was used by W. van der Kallen to give a group structure on the orbit set $$\frac{Um_{n}(R)}{E_{n}(R)}$$ commutative noetherian ring of dimension $$d\le 2n-4.$$ In this paper, we generalise $$m\times n $$ right invertible matrices

We use descent theoretic methods to solve the homotopy limit problem for Hermitian $K$-theory over quasi-compact and quasi-separated base schemes. As another application of these methods, we compute cellular Picard group 2-complete $\mathop{Spec}(\mathbb{C})$, showing that only invertible spectra are suspensions tensor unit.

A linear 2-All-or-Nothing Transform can be considered as an invertible matrix with all 2 × 2 submatrices invertible. It is known [P. D’Arco, N. Nasr Esfahani and D.R. Stinson, Electron. J. Combin. 23(4) (2016), #P4.10] that there is no binary s×s matrix that satisfies these conditions, for s > 2. In this paper, different computational methods for generating invertible binary matrices with close...

We study one-sided substitution subshifts, and how they can be respresented using Bratteli-Vershik systems. In particular we focus on minimal recognizable substitutions such that the generated one-sided substitution subshift contains only one non-shift-invertible element, and we call these substitutions quasi-invertible. We characterise these substitutions, and show that if the substitution is ...