Partitions of unity in SL(2, Z), negative continued fractions, and dissections of polygons

被引：0

作者：

Ovsienko, Valentin ^{[1
]}

机构：

[1] CNRS, Lab Math UFR Sci Exactes & Nat, Moulin Housse,BP 1039, F-51687 Reims 2, France

来源：

RESEARCH IN THE MATHEMATICAL SCIENCES | 2018年 / 5卷

关键词：

DIFFERENCE-OPERATORS; PATTERNS; FRIEZES;

D O I：

10.1007/s40687-018-0139-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize sequences of positive integers (a(1), a(2), ... , a(n)) for which the 2 x 2 matrix [GRAPHICS] is either the identity matrix Id, its negative - Id, or square root of - Id. This extends a theorem of Conway and Coxeter that classifies such solutions subject to a total positivity restriction.

引用

页数：25

共 10 条

[1] Partitions of unity in SL(2,Z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {SL}(2,\mathbb Z)$$\end{document}, negative continued fractions, and dissections of polygons
Valentin Ovsienko
Research in the Mathematical Sciences, 2018, 5 (2)
[2] CONTINUED FRACTIONS WITH SL(2, Z)-BRANCHES: COMBINATORICS AND ENTROPY
Carminati, Carlo
Isola, Stefano
Tiozzo, Giulio
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 370 (07) : 4927 - 4973
[3] CONTINUED FRACTIONS AND THE CONJUGACY PROBLEM IN SL2(Z)
APPELGATE, H
ONISHI, H
COMMUNICATIONS IN ALGEBRA, 1981, 9 (11) : 1121 - 1130
[4] Continued fractions associated with SL3 (Z) and units in complex cubic fields
Vulakh, LY
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2002, 54 (06): : 1305 - 1318
[5] HEAP-ORDERED TREES, 2-PARTITIONS AND CONTINUED FRACTIONS
CHEN, WC
NI, WC
EUROPEAN JOURNAL OF COMBINATORICS, 1994, 15 (06) : 513 - 517
[6] Classification of new continued fractions attached to a R(z) operation in a unity close to excess.
Cahen, A
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1924, 178 : 2230 - 2232
[7] SUBGROUPS OF SL2(Z) CHARACTERIZED BY CERTAIN CONTINUED FRACTION REPRESENTATIONS
Han, Sandie
Masuda, Ariane M.
Singh, Satyanand
Thiel, Johann
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2020, 148 (09) : 3775 - 3786
[8] DYNAMICS OF THE CONTINUED-FRACTION MAP AND THE SPECTRAL THEORY OF SL(2, Z)
EFRAT, I
INVENTIONES MATHEMATICAE, 1993, 114 (01) : 207 - 218
[9] ON THE CONTINUED FRACTIONS KO-GAMMA-O+KO(K-N(1-GAMMA-N-GAMMA-(-)N) .Z GAMMA-(-)N2-1 KN+1 GAMMA-N+1
FRANK, E
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1948, 54 (11) : 1061 - 1061
[10] Functions f from Fn p, n=2m, to Z pk for which the character sum Hk f (pt, u) = ∼ x.Fn p. ptf (x) pk. u. x p (where.q=e2pi/ q is a q-th root of unity), has absolute value pm for all u. Fn p and 0=t = k-1, induce relative difference sets in Fn p x Z pk hence are called bent. Functions only necessarily satisfying |Hk f (1, u)| = pm are called generalized bent. We show that with spreads we not only can construct a variety of bent and generalized bent functions, but also can design functions from Fn p to Zpm satisfying |Hm f (pt, u)| = pm if and only if t. T for any T. {0, 1..., m-1}. A generalized bent function can also be seen as a Boolean (p-ary) bent function together with a partition of Fn p with certain properties. We show that the functions from the completed Maiorana-McFarland class are bent functions, which allow the largest possible partitions.
Meidl, Wilfried
Pott, Alexander
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2019, 11 (06): : 1233 - 1245

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