Search results for "CoDi"
showing 10 items of 1391 documents
Varieties of almost polynomial growth: classifying their subvarieties
2007
Let G be the infinite dimensional Grassmann algebra over a field F of characteristic zero and UT2 the algebra of 2 x 2 upper triangular matrices over F. The relevance of these algebras in PI-theory relies on the fact that they generate the only two varieties of almost polynomial growth, i.e., they grow exponentially but any proper subvariety grows polynomially. In this paper we completely classify, up to PI-equivalence, the associative algebras A such that A is an element of Var(G) or A is an element of Var(UT2).
Matrix algebras of polynomial codimension growth
2007
We study associative algebras with unity of polynomial codimension growth. For any fixed degree $k$ we construct associative algebras whose codimension sequence has the largest and the smallest possible polynomial growth of degree $k$. We also explicitly describe the identities and the exponential generating functions of these algebras.
Polynomial growth of the codimensions: a characterization
2009
Let A A be a not necessarily associative algebra over a field of characteristic zero. Here we characterize the T-ideal of identities of A A in case the corresponding sequence of codimensions is polynomially bounded.
An almost nilpotent variety of exponent 2
2013
We construct a non-associative algebra A over a field of characteristic zero with the following properties: if V is the variety generated by A, then V has exponential growth but any proper subvariety of V is nilpotent. Moreover, by studying the asymptotics of the sequence of codimensions of A we deduce that exp(V) = 2.
A simple algorithm for generating neuronal dendritic trees
1990
Abstract A simple, efficient algorithm is presented for generating the codewords of all neuronal dendritic trees with a given number of terminal nodes. Furthermore, a procedure is developed for deciding if different codewords correspond to topologically equivalent trees.
Burrows-Wheeler transform and Run-Length Enconding
2017
In this paper we study the clustering effect of the Burrows-Wheeler Transform (BWT) from a combinatorial viewpoint. In particular, given a word w we define the BWT-clustering ratio of w as the ratio between the number of clusters produced by BWT and the number of the clusters of w. The number of clusters of a word is measured by its Run-Length Encoding. We show that the BWT-clustering ratio ranges in ]0, 2]. Moreover, given a rational number \(r\,\in \,]0,2]\), it is possible to find infinitely many words having BWT-clustering ratio equal to r. Finally, we show how the words can be classified according to their BWT-clustering ratio. The behavior of such a parameter is studied for very well-…
On almost nilpotent varieties of subexponential growth
2015
Abstract Let N 2 be the variety of left-nilpotent algebras of index two, that is the variety of algebras satisfying the identity x ( y z ) ≡ 0 . We introduce two new varieties, denoted by V sym and V alt , contained in the variety N 2 and we prove that V sym and V alt are the only two varieties almost nilpotent of subexponential growth.
Characterizing varieties of colength ≤4
2009
Let A be an associative algebra over a field F of characteristic zero, and let χ n (A), n = 1,2,…, be the sequence of cocharacters of A. For every n ≥ 1, let l n (A) denote the nth colength of A, counting the number of S n -irreducibles appearing in χ n (A). In this article, we classify the algebras A such that the sequence of colengths l n (A), n = 1,2,…, is bounded by four. Moreover we construct a finite number of algebras A 1,…, A d , such that l n (A) ≤ 4 if and only if A 1,…, A d ∉ var(A).
Polynomial identities on superalgebras and exponential growth
2003
Abstract Let A be a finitely generated superalgebra over a field F of characteristic 0. To the graded polynomial identities of A one associates a numerical sequence {cnsup(A)}n⩾1 called the sequence of graded codimensions of A. In case A satisfies an ordinary polynomial identity, such sequence is exponentially bounded and we capture its exponential growth by proving that for any such algebra lim n→∞ c n sup (A) n exists and is a non-negative integer; we denote such integer by supexp(A) and we give an effective way for computing it. As an application, we construct eight superalgebras Ai, i=1,…,8, characterizing the identities of any finitely generated superalgebra A with supexp(A)>2 in the f…
Proper identities, Lie identities and exponential codimension growth
2008
Abstract The exponent exp ( A ) of a PI-algebra A in characteristic zero is an integer and measures the exponential rate of growth of the sequence of codimensions of A [A. Giambruno, M. Zaicev, On codimension growth of finitely generated associative algebras, Adv. Math. 140 (1998) 145–155; A. Giambruno, M. Zaicev, Exponential codimension growth of P.I. algebras: An exact estimate, Adv. Math. 142 (1999) 221–243]. In this paper we study the exponential rate of growth of the sequences of proper codimensions and Lie codimensions of an associative PI-algebra. We prove that the corresponding proper exponent exists for all PI-algebras, except for some algebras of exponent two strictly related to t…