Additive Representation for Preferences Over Menus in Finite Choice Settings

2010 ◽  
Author(s):  
Leandro Gorno
Keyword(s):  
Additive Representation ◽  
Finite Choice

scholarly journals On winning shifts of marked uniform substitutions

2019 ◽  
Vol 53 (1-2) ◽  
pp. 51-66 ◽  
Author(s):  
Jarkko Peltomäki ◽  
Ville Salo
Keyword(s):  
Winning Strategy ◽  
Explicit Description ◽  
Finite Alphabet ◽  
Combinatorics On Words ◽  
Simple Derivation ◽  
Choice Sequence ◽  
Target Set ◽  
Finite Choice

The second author introduced with I. Törmä a two-player word-building game [Fund. Inform. 132 (2014) 131–152]. The game has a predetermined (possibly finite) choice sequence α1, α2, … of integers such that on round n the player A chooses a subset Sn of size αn of some fixed finite alphabet and the player B picks a letter from the set Sn. The outcome is determined by whether the word obtained by concatenating the letters B picked lies in a prescribed target set X (a win for player A) or not (a win for player B). Typically, we consider X to be a subshift. The winning shift W(X) of a subshift X is defined as the set of choice sequences for which A has a winning strategy when the target set is the language of X. The winning shift W(X) mirrors some properties of X. For instance, W(X) and X have the same entropy. Virtually nothing is known about the structure of the winning shifts of subshifts common in combinatorics on words. In this paper, we study the winning shifts of subshifts generated by marked uniform substitutions, and show that these winning shifts, viewed as subshifts, also have a substitutive structure. Particularly, we give an explicit description of the winning shift for the generalized Thue–Morse substitutions. It is known that W(X) and X have the same factor complexity. As an example application, we exploit this connection to give a simple derivation of the first difference and factor complexity functions of subshifts generated by marked substitutions. We describe these functions in particular detail for the generalized Thue–Morse substitutions.

On the k-th difference of an additive representation function

2011 ◽  
Vol 48 (1) ◽  
pp. 93-103
Author(s):  
Sándor Kiss
Keyword(s):  
Infinite Sequence ◽  
Probabilistic Methods ◽  
Number Of Solutions ◽  
Fixed Integer ◽  
Representation Function ◽  
Additive Representation ◽  
Consecutive Integers ◽  
Additive Representation Function ◽  
Positive Integers

Let k ≧ 2 be a fixed integer, A = {a1, a2, …} (a1 < a2 < …) be an infinite sequence of positive integers, and let Rk(n) denote the number of solutions of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$a_{i_1 } + a_{i_2 } + \cdots + a_{i_k } = n,a_{i_1 } \in \mathcal{A},...,a_{i_k } \in \mathcal{A}$$ \end{document}. Let B(A, N) denote the number of blocks formed by consecutive integers in A up to N. In [5], it was proved that if k > 2 and \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\lim _{N \to \infty } \frac{{B(\mathcal{A},N)}}{{\sqrt[k]{N}}}$$ \end{document} = ∞ then |δl(Rk(n))| cannot be bounded for l ≦ k. The aim of this paper is to show that the above result is nearly best possible. We are using probabilistic methods.

scholarly journals Additive representation in thin sequences, II: The binary Goldbach problem

Mathematika ◽  
2000 ◽  
Vol 47 (1-2) ◽  
pp. 117-125 ◽  
Author(s):  
J. Brüdern ◽  
K. Kawada ◽  
T. D. Wooley
Keyword(s):  
Additive Representation ◽  
Goldbach Problem

Properties of an atom–bond additive representation of the interaction for benzene–argon clusters

2004 ◽  
Vol 392 (4-6) ◽  
pp. 514-520 ◽  
Author(s):  
M Albertı́ ◽  
A Castro ◽  
A Laganà ◽  
F Pirani ◽  
M Porrini ◽  
...  
Keyword(s):  
Additive Representation ◽  
Argon Clusters ◽  
Atom Bond

scholarly journals Additive representation in thin sequences, V: Mixed problems of Waring's type

2003 ◽  
Vol 92 (2) ◽  
pp. 181
Author(s):  
J Brüdern ◽  
K. Kawada ◽  
T. D. Wooley
Keyword(s):  
Additive Representation ◽  
Mixed Problems
Sign in / Sign up

Export Citation Format

Share Document