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Information of the project and the call

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

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