Combinatorial Etude

• Autorzy: Stoenchev Miroslav , Todorov Venelin

Identyfikatory

DOI

10.15439/2021F121

• Konferencja: Federated Conference on Computer Science and Information Systems (16 ; 02-05.09.2021 ; online)
• Języki publikacji: EN

Abstrakty

EN

The purpose of this article is to consider a special class of combinatorial problems, the so called Prouhet-Tarry Escot problem, solution of which is realized by constructing finite sequences of ±1. For example, for fixed p∈N, is well known the existence of np∈N with the property: any set of np consecutive integers can be divided into 2 sets, with equal sums of its p[th] powers. The considered property remains valid also for sets of finite arithmetic progressions of complex numbers.

Słowa kluczowe

EN

arithmetic; combinatorial mathematics; computational complexity; functional analysis; graph theory; number theory; sequences; set theory

PL

arytmetyka; matematyka kombinatoryczna; złożoność obliczeniowa; analiza funkcjonalna; teoria grafów; teoria liczb; sekwencje; teoria mnogości

• Wydawca: Polskie Towarzystwo Informatyczne
• Czasopismo: Annals of Computer Science and Information Systems
• Rocznik: 2021
• Tom: Vol. 25
• Strony: 231--234
• Opis fizyczny: Bibliogr. 8 poz., wz.

Twórcy

autor

Stoenchev Miroslav

• Technical Universityof Sofia,Bulgaria

autor

Todorov Venelin

• Institute of Mathematics and Informatics, Bulgarian Academyof Sciences
• Institute of Information and Communication Technologies, Bulgarian Academy of Sciences

Bibliografia

• 1. J.-P. Allouche, J. O. Shallit, The ubiquitous Prouhet-Thue-Morse sequence. In C. Ding, T. Helleseth, and H. Niederreiter, editors, Sequences and Their Applications, Proceedings of SETA ’98, pp. 1–16, Springer-Verlag, 1999.
• 2. P. Borwein, C. Ingalls, The Prouhet-Tarry-Escott Problem revisited. Enseign. Math. 40 (1994), 3–27. MR 95d:11038
• 3. P. Borwein, Computational Excursions in Analysis and Number Theory, Springer-Verlag, New York, 2002.
• 4. J. Byszewski and M. Ulas, Some identitites involving the Prouhet-Thue-Morse sequence and its relatives, Acta Math. Hungar., 127-2,438-456, 2015
• 5. H. L. Dorwart and O. E. Brown, The Tarry-Escott Problem, M. A. A. Monthly, 44, 613-626, 1937
• 6. G. H. Hardy, E. M. Wright, An Introduction to the Theory of Numbers, fifth ed., Oxford Univ. Press, New York,1979
• 7. M. Stoenchev, V. Todorov, Combinatorial etudes and number theory, (in appear)
• 8. T. Wakhare, C. Vignat, Settling some sum suppositions, https://arxiv.org/abs/1805.10569/

Uwagi

1. Track 1: Artificial Intelligence in Applications

2. Session: 14th International Workshop on Computational Optimization

3. Short Paper