Multi-dimensional versions of a theorem of Fine and Wilf and a formula of Sylvester

DOI10.1090/S0002-9939-03-06970-3zbMath1013.05087OpenAlexW1953069975MaRDI QIDQ4794563

Robert Tijdeman, R. Jamie Simpson

Publication date: 19 February 2003

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-03-06970-3

zbMATH Keywords

latticeperiodicityFrobeniusperiodicity lemmahyperfacescoin-changingformula of SylvesterFrobenius' coin-changing problemtheorem of Fine and Wilf

Mathematics Subject Classification ID

Combinatorics on words (68R15) Other combinatorial number theory (11B75) Free lattices, projective lattices, word problems (06B25) Extremal combinatorics (05D99) Elementary number theory (11Axx)

Related Items (12)

Substitutions, abstract number systems and the space filling property ⋮ THE FROBENIUS VECTOR OF A FREE AFFINE SEMIGROUP ⋮ Lattices and multi-dimensional words ⋮ LLL-reduction for integer knapsacks ⋮ The Frobenius postage stamp problem, and beyond ⋮ Fine and Wilf words for any periods ⋮ Maximal continuants and the Fine-Wilf theorem ⋮ Intersecting periodic words ⋮ MULTIPSEUDOPERIODIC WORDS ⋮ A multidimensional critical factorization theorem ⋮ Rauzy substitutions and multi-dimensional Sturmian words ⋮ A discrete structure with the minimal set

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Rauzy fractal
• Skolem's solution to a problem of Frobenius
• Fine and Wilf's theorem for three periods and a generalization of Sturmian words
• Fine and Wilf words for any periods
• On Fine and Wilf's theorem for bidimensional words.
• On a paper by Castelli, Mignosi, Restivo
• On the linear diophantine problem of Frobenius.
• On a linear Diophantine problem of Frobenius.
• Uniqueness Theorems for Periodic Functions

This page was built for publication: Multi-dimensional versions of a theorem of Fine and Wilf and a formula of Sylvester