Related papers: The Structure of Z-related sets
To present a survey on known results from the theory of transposed Poisson algebras, as well as to establish new results on this subject, are the main aims of the present paper. Furthermore, a list of open questions for future research is…
We present a diagram surveying equivalence or strict implication for properties of different nature (algebraic, model theoretic, topological, etc.) about groups definable in o-minimal structures. All results are well-known and an extensive…
We give a purely algebraic treatment of reduction theory for connections over the formal punctured disc. Our proofs apply to arbitrary connected linear algebraic groups over an algebraically closed field of characteristic 0. We also state…
We compute the expected number of commutations appearing in a reduced word for the longest element in the symmetric group. The asymptotic behavior of this value is analyzed and shown to approach the length of the permutation, meaning that…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
Many neural nets appear to represent data as linear combinations of "feature vectors." Algorithms for discovering these vectors have seen impressive recent success. However, we argue that this success is incomplete without an understanding…
We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.
Recently an action formulation, called the general WZW orbifold action, was given for each sector of every WZW orbifold. In this paper we gauge this action by general twisted gauge groups to find the action formulation of each sector of…
What sets A \subset Z^n can be written in the form (K-K) \cap Z^n, where K is a compact subset of R^n such that K+Z^n=R^n? Such sets A are called achievable, and it is known that if A is achievable, then < A >=Z^n. This condition completely…
A relationship between the Riemann zeta function and a density on integer sets is explored. Several properties of the examined density are derived.
We show that the compositions of positive integers may be interpreted in terms of powers of some power series, over arbitrary commutative ring. As consequences, several closed formulas for the compositions as well as for the generalized…
We present an overview of selected topics in random permutations and random partitions highlighting analogies with random matrix theory.
In this note we show that pattern matching in permutations is polynomial time reducible to pattern matching in set partitions. In particular, pattern matching in set partitions is NP-Complete.
We show that $ZF+DC+$"all Turing invariant sets of reals have the perfect set property" implies that all sets of reals have the perfect set property. We also show that this result generalizes to all countable analytic equivalence relations.
This is the first paper in a sequence devoted to giving manifestly non-negative formulas for generalized exponents of small representations in all types. The main part of this paper illustrates the overall structure of the argument on root…
We demonstrate that statistics for several types of set partitions are described by generating functions which appear in the theory of integrable equations.
The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…
The regular representation is related to Zhu's $A(V)$-theory and an induced module from an $A(V)$-module to a $V$-module is defined in terms of the regular representation. As an application, a new proof of Frenkel and Zhu's fusion rule…
We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…
We compute the completion of the groups SL_n(Z[t]) and SL_n(Z[t,t^{-1}]) relative to the obvious homomorphisms to SL_n(Q); this is a generalization of the classical Malcev completion. We also make partial computations of the rational second…