Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

Equipment

Delete all

Arithmetic properties of special integer sequences, polynomials, and continued fractions

2019/34/E/ST1/00094

Keywords:

partition polynomials composition polynomials automatic sequences continued fractions prime numbers

Descriptors:

  • ST1_003:
  • ST1_014:

Panel:

ST1 - Mathematics: all areas of mathematics, pure and applied, as well as mathematical foundations of computer science, physics and statistics

Host institution :

Uniwersytet Jagielloński, Wydział Matematyki i Informatyki

woj. małopolskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

dr hab. Maciej Ulas 

Number of co-investigators in the project: 5

Call: SONATA BIS 9 - announced on 2019-06-17

Amount awarded: 815 381 PLN

Project start date (Y-m-d): 2020-04-10

Project end date (Y-m-d): 2026-04-09

Project duration:: 72 months (the same as in the proposal)

Project status: Pending project

Project description

Download the project description in a pdf file

Note - project descriptions were prepared by the authors of the applications themselves and placed in the system in an unchanged form.

Information in the final report

  • Publication in academic press/journals (31)
  • Articles in post-conference publications (1)
  1. Divisibility and Arithmetic Properties of a Class of Sparse Polynomials
    Authors:
    Karl Dilcher, Maciej Ulas
    Academic press:
    INTEGERS (rok: 2022, tom: 22, strony: A8)
    Status:
    Published
    DOI:
    DOI - link to the publication
  2. Log-concavity of the restricted partition function $p_\mathcal{A}(n,k)$ and the new Bessenrodt-Ono type inequality
    Authors:
    Krystian Gajdzica
    Academic press:
    Journal of number theory (rok: 2023, tom: 251, strony: 31-65), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jnt.2023.04.001 - link to the publication
  3. Restricted partition functions and the r-log-concavity of quasi-polynomial-like functions
    Authors:
    Krystian Gajdzica
    Academic press:
    Acta Arithmetica (rok: 2025, tom: 217 (1), strony: 67-94), Wydawca: IMPAN
    Status:
    Published
    DOI:
    10.4064/aa231101-30-6 - link to the publication
  4. Values of binary partition function represented by a sum of three squares
    Authors:
    Bartosz Sobolewski, Maciej Ulas
    Academic press:
    Results in Mathematics (rok: 2023, tom: 78, strony: Article 188), Wydawca: SPringer
    Status:
    Published
    DOI:
    10.1007/s00025-023-01966-8 - link to the publication
  5. Some Properties of a Class of Sparse Polynomials
    Authors:
    Karl Dilcher, Maciej Ulas
    Academic press:
    Journal of Mathematical Analysis and Applications (rok: 2022, tom: 505 (1), strony: 125449), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2021.125449 - link to the publication
  6. Equal values of certain partition functions via Diophantine equations
    Authors:
    Szabolcs Tengely, Maciej Ulas
    Academic press:
    Research in Number Theory (rok: 2021, tom: 7, strony: Article Number: 67), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s40993-021-00293-7 - link to the publication
  7. Some Properties of a Class of Sparse Polynomials
    Authors:
    Karl Dilcher, Maciej Ulas
    Academic press:
    Journal of Mathematical Analysis and Applications (rok: 2022, tom: 505 (1), strony: 125449), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2021.125449 - link to the publication
  8. On Kakeya Conditions for Achievement Sets
    Authors:
    Jacek Marchwicki, Piotr Miska
    Academic press:
    Results in Mathematics (rok: 2021, tom: 76(4), strony: Article number: 181), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00025-021-01479-2 - link to the publication
  9. More on Kakeya-like conditions
    Authors:
    Piotr Miska, Franciszek Prus-Wiśniowski, Jolanta Ptak
    Academic press:
    Results in Mathematics (rok: 2023, tom: 78, strony: 113), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00025-023-01890-x - link to the publication
  10. Equal values of certain partition functions via Diophantine equations
    Authors:
    Szabolcs Tengely, Maciej Ulas
    Academic press:
    Research in Number Theory (rok: 2021, tom: 7, strony: Article Number: 67), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s40993-021-00293-7 - link to the publication
  11. Signs behaviour of sums of weighted numbers of compositions
    Authors:
    Filip Gawron, Maciej Ulas
    Academic press:
    Ramanujan Journal (rok: 2025, tom: 66, strony: 32), Wydawca: Springer Nature
    Status:
    Published
    DOI:
    10.1007/s11139-024-01006-1 - link to the publication
  12. The Turán and Laguerre inequalities for quasi-polynomial-like functions
    Authors:
    Krystian Gajdzica
    Academic press:
    Research in number theory (rok: 2024, tom: 10, strony: 46), Wydawca: Springer Nature
    Status:
    Published
    DOI:
    10.1007/s40993-024-00532-7 - link to the publication
  13. Binomial Coefficients, Roots of Unity and Powers of Prime Numbers
    Authors:
    Piotr Miska
    Academic press:
    Bulletin of the Malaysian Mathematical Sciences Society (rok: 2022, tom: 45, strony: 1489 - 1506), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s40840-022-01266-4 - link to the publication
  14. A Fibonacci type sequence with Prouhet-Thue-Morse coefficients
    Authors:
    Eryk Lipka, Maciej Ulas
    Academic press:
    Journal of Difference Equations and Applications (rok: 2022, tom: 28 (5), strony: 695-715), Wydawca: Taylor and Francis
    Status:
    Published
    DOI:
    10.1080/10236198.2022.2065918 - link to the publication
  15. Solutions of certain meta-Fibonacci recurrences
    Authors:
    Bartosz Sobolewski, Maciej Ulas
    Academic press:
    Acta Arithmetica (rok: 2023, tom: 209, strony: 269-289), Wydawca: Instytut Matematyczny PAN
    Status:
    Published
    DOI:
    10.4064/aa220613-19-1 - link to the publication
  16. Signs behaviour of sums of weighted numbers of partitions
    Authors:
    Filip Gawron, Maciej Ulas
    Academic press:
    Ramanujan Journal (rok: 2023, tom: 60, strony: 571–584), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11139-022-00602-3 - link to the publication
  17. Log-concavity of the restricted partition function $p_\mathcal{A}(n,k)$ and the new Bessenrodt-Ono type inequality
    Authors:
    Krystian Gajdzica
    Academic press:
    Journal of number theory (rok: 2023, tom: 251, strony: 31-65), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jnt.2023.04.001 - link to the publication
  18. On continued fraction coefficients of square roots of primes
    Authors:
    Vitezeslav Kala, Piotr Miska
    Academic press:
    Journal of Number Theory (rok: 2022, tom: 253, strony: 215-234), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jnt.2023.06.013 - link to the publication
  19. Representing generalized derangements as sums of three squares
    Authors:
    Maciej Ulas
    Academic press:
    Fibonacci Quarterly (rok: 2023, tom: 61(3), strony: 231-240), Wydawca: The Fibonacci Association
    Status:
    Published
  20. Unususal class of polynomials related to partitions
    Authors:
    Błażej Żmija
    Academic press:
    Ramanujan Journal (rok: 2023, tom: 62, strony: 1069–1080), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11139-023-00739-9 - link to the publication
  21. Binomial Coefficients, Roots of Unity and Powers of Prime Numbers
    Authors:
    Piotr Miska
    Academic press:
    Bulletin of the Malaysian Mathematical Sciences Society (rok: 2022, tom: 45, strony: 1489 - 1506), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s40840-022-01266-4 - link to the publication
  22. On $k$-regularity of sequences of valuations and last nonzero digits
    Authors:
    Bartosz Sobolewski
    Academic press:
    Ramanujan Journal (rok: 2023, tom: 61, strony: 1151-1195), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11139-023-00710-8 - link to the publication
  23. A note on the restricted partition function $p_\mathcal{A}(n,k)$
    Authors:
    Krystian Gajdzica
    Academic press:
    Discrete Mathematics (rok: 2022, tom: 345 (9), strony: 112943), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.disc.2022.112943 - link to the publication
  24. Some observations and speculations on partitions into $d$-th powers
    Authors:
    Maciej Ulas
    Academic press:
    Bulletin of the Australian Mathematical Society (rok: 2021, tom: 104, strony: 406-414), Wydawca: Cambridge University Press
    Status:
    Published
    DOI:
    10.1017/S0004972721000034 - link to the publication
  25. Geometric progressions in the sets of values of rational functions
    Authors:
    Maciej Ulas
    Academic press:
    Indagationes Mathematicae (rok: 2024, tom: 35 (4), strony: 622-637), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.indag.2023.08.005 - link to the publication
  26. A note on the restricted partition function $p_\mathcal{A}(n,k)$
    Authors:
    Krystian Gajdzica
    Academic press:
    Discrete Mathematics (rok: 2022, tom: 345 (9), strony: 112943), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.disc.2022.112943 - link to the publication
  27. Stirling numbers and periodic points
    Authors:
    Thomas Ward, Piotr Miska
    Academic press:
    Acta Arithmetica (rok: 2021, tom: 201, strony: 421-435), Wydawca: IMPAN
    Status:
    Published
    DOI:
    10.4064/aa210309-9-8 - link to the publication
  28. On the Bessenrodt–Ono type inequality for a wide class of A-partition functions
    Authors:
    Krystian Gajdzica
    Academic press:
    Ramanujan Journal (rok: 2025, tom: 66, strony: 80), Wydawca: Springer Nature
    Status:
    Published
    DOI:
    10.1007/s11139-025-01048-z - link to the publication
  29. On two conjectures regarding generalized sequence of derangements
    Authors:
    Eryk Lipka, Florian Luca, Piotr Miska
    Academic press:
    Funct. Approx. Comment. Math. (rok: 2022, tom: 67 (2), strony: 223-234), Wydawca: Adam Mickiewicz University
    Status:
    Published
    DOI:
    10.7169/facm/1989 - link to the publication
  30. Diophantine problems related to cyclic cubic and quartic fields
    Authors:
    Szabolcs Tengely, Maciej Ulas
    Academic press:
    Journal of Number Theory (rok: 2022, tom: 240, strony: 656 - 684), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jnt.2022.01.003 - link to the publication
  31. Binomial coefficients, roots of unity and powers of prime numbers
    Authors:
    Piotr Miska
    Status:
    Accepted for publication
  1. Geometric Progressions in the Sets of Values of Reducible Cubic Forms
    Authors:
    Bartłomiej Głowacki, Maciej Ulas
    Conference:
    Combinatorial and Additive Number Theory VI (rok: 2025, tom: Combinatorial and Additive Number Theory, 2023, strony: 205-219), Wydawca: Springer
    Data:
    konferencja 23-25 maja 2023
    Status:
    Published
    DOI:
    10.1007/978-3-031-65064-2_9 - link to the publication

O Narodowym Centrum Nauki

Finansowanie nauki

Współpraca zagraniczna

Centrum prasowe

Deklaracja dostępności
Przetwarzanie danych osobowych
Polityka cookies

Partnerzy