Related papers: Correction: Root extraction in one-relator groups …
This is an appendix to our paper "An update of the Hirsch Conjecture" (arXiv:0907.1186), containing proofs of some of the results and comments that were omitted in it.
This document is the first iteration of an attempt to collate information about small-rank groups of Lie type over small fields, and their representation theory over the defining field. This information is important in the author's work on…
We further develop the notion of perinormality from our last paper, showing that it is preserved by many pullback constructions. In doing so, we introduce the concepts of relative perinormality and fragility for ring extensions.
This paper has been withdrawn by the author due to an error in the proof of Proposition 4.8.
We introduce the notion of categorical absorption of singularities: an operation that removes from the derived category of a singular variety a small admissible subcategory responsible for singularity and leaves a smooth and proper…
A short note that contains some Cliff's notes of the general theory (see math.AG/9905103) but concentrates on one of the stranger aspects of it - existence of other irreducible components.
We provide a new representation-independent formulation of Occam's razor theorem, based on Kolmogorov complexity. This new formulation allows us to: (i) Obtain better sample complexity than both length-based and VC-based versions of Occam's…
This paper has been withdrawn to address an omission. It will be resubmitted in the near future.
This paper has been withdrawn due to a error in Theorem 3.1.
This note contains additions to the paper 'Clustered cell decomposition in P-minimal structures' (arXiv:1612.02683). We discuss a question which was raised in that paper, on the order of clustered cells. We also consider a notion of cells…
Complex machine learning algorithms are used more and more often in critical tasks involving text data, leading to the development of interpretability methods. Among local methods, two families have emerged: those computing importance…
The paper gives a short account of the contents of "Regular Algebraic K-Theory For Groups" by the author and its connections with other homology and K-theories.
For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroup. The factorizations are an extension of Dedekind's theorem. The extension leads to a generalization of Dedekind's…
Existing research studies on cross-sentence relation extraction in long-form multi-party conversations aim to improve relation extraction without considering the explainability of such methods. This work addresses that gap by focusing on…
An technically interesting proof of a known theorem.
Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.
This purpose of this letter is to handle a gap that was found in the proof of Theorem 2 in the paper "The generalized stochastic likelihood decoder: random coding and expurgated bounds."
This article focuses on the study of cut groups, i.e., the groups which have only trivial central units in their integral group ring. We provide state of art for cut groups. The results are compiled in a systematic manner and have also been…
We prove some extensions of Andrews inequality.
The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…