Description of normal bases of boundary algebras and factor languages of slow growth

A. Ya Belov; A. L. Chernyat’ev

doi:10.1134/s0001434617010242

Description of normal bases of boundary algebras and factor languages of slow growth

A. Ya Belov, A. L. Chernyat’ev

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

For an algebra A, denote by V_A(n) the dimension of the vector space spanned by the monomials whose length does not exceed n. Let T_A(n) = V_A(n) − V_A(n − 1). An algebra is said to be boundary if T_A(n) − n < const. In the paper, the normal bases are described for algebras of slow growth or for boundary algebras. Let L be a factor language over a finite alphabet A. The growth function T_L(n) is the number of subwords of length n in L. We also describe the factor languages such that T_L(n) ≤ n + const.

Original language	English
Pages (from-to)	203-207
Number of pages	5
Journal	Mathematical Notes
Volume	101
Issue number	1-2
DOIs	https://doi.org/10.1134/s0001434617010242
State	Published - 1 Jan 2017

Keywords

Sturm sequence
factor language
growth function
monomial algebra
normal basis

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1134/s0001434617010242

Cite this

@article{fa3c27e9029449dc92fef628bf473d5e,

title = "Description of normal bases of boundary algebras and factor languages of slow growth",

abstract = "For an algebra A, denote by VA(n) the dimension of the vector space spanned by the monomials whose length does not exceed n. Let TA(n) = VA(n) − VA(n − 1). An algebra is said to be boundary if TA(n) − n < const. In the paper, the normal bases are described for algebras of slow growth or for boundary algebras. Let L be a factor language over a finite alphabet A. The growth function TL(n) is the number of subwords of length n in L. We also describe the factor languages such that TL(n) ≤ n + const.",

keywords = "Sturm sequence, factor language, growth function, monomial algebra, normal basis",

author = "Belov, {A. Ya} and Chernyat{\textquoteright}ev, {A. L.}",

note = "Publisher Copyright: {\textcopyright} 2017, Pleiades Publishing, Ltd.",

year = "2017",

month = jan,

day = "1",

doi = "10.1134/s0001434617010242",

language = "الإنجليزيّة",

volume = "101",

pages = "203--207",

journal = "Mathematical Notes",

issn = "0001-4346",

publisher = "Pleiades Publishing",

number = "1-2",

}

TY - JOUR

T1 - Description of normal bases of boundary algebras and factor languages of slow growth

AU - Belov, A. Ya

AU - Chernyat’ev, A. L.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - For an algebra A, denote by VA(n) the dimension of the vector space spanned by the monomials whose length does not exceed n. Let TA(n) = VA(n) − VA(n − 1). An algebra is said to be boundary if TA(n) − n < const. In the paper, the normal bases are described for algebras of slow growth or for boundary algebras. Let L be a factor language over a finite alphabet A. The growth function TL(n) is the number of subwords of length n in L. We also describe the factor languages such that TL(n) ≤ n + const.

AB - For an algebra A, denote by VA(n) the dimension of the vector space spanned by the monomials whose length does not exceed n. Let TA(n) = VA(n) − VA(n − 1). An algebra is said to be boundary if TA(n) − n < const. In the paper, the normal bases are described for algebras of slow growth or for boundary algebras. Let L be a factor language over a finite alphabet A. The growth function TL(n) is the number of subwords of length n in L. We also describe the factor languages such that TL(n) ≤ n + const.

KW - Sturm sequence

KW - factor language

KW - growth function

KW - monomial algebra

KW - normal basis

UR - http://www.scopus.com/inward/record.url?scp=85015622926&partnerID=8YFLogxK

U2 - 10.1134/s0001434617010242

DO - 10.1134/s0001434617010242

M3 - مقالة

SN - 0001-4346

VL - 101

SP - 203

EP - 207

JO - Mathematical Notes

JF - Mathematical Notes

IS - 1-2

ER -

Description of normal bases of boundary algebras and factor languages of slow growth

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this