Strona: Publikacje / Zakład Matematyki Dyskretnej

1. A. Szynal-Liana, I. Włoch, Oresme hybrid numbers and hybrationals, Kragujevac Journal of Mathematics, 48(5) (2024), 747-753 (w druku)
2. D. Bród, A. Szynal-Liana, On some Combinatorial Properties of Generalized Commutative Pell and Pell-Lucas Quaternions, Kragujevac Journal of Mathematics, 49(6) (2025), 889–897 (w druku)
3. P. Bednarz, A. Szynal-Liana, Bihyperbolic numbers of the Fibonacci type and triangular matrices (tables), Azerbaijan Journal of Mathematics, (2024) (w druku)
4. M. Rubajczyk, A. Szynal-Liana, Cobalancing hybrid numbers, Annales UMCS (w druku)
5. D. Bród, A. Szynal-Liana, I. Włoch, On a new generalization of Pell hybrid numbers, Annales Mathematicae Silesianae (w druku)

1. P. Bednarz, M. Pirga, On Proper 2-Dominating Sets in Graphs , Symmetry (2024), 16, 296. https://doi.org/10.3390/sym16030296.
2. U. Bednarz, M. Wołowiec-Musiał, Generalized Fibonacci-Leonardo Numbers, Journal of Difference Equations and Applications, (2024), 111-121, http://doi.org/10.1080/10236198.2023.2265509
3. D. Bród, A. Szynal-Liana, On generalized bihyperbolic Mersenne numbers, Mathematica Bohemica 149, No. 1 (2024), 75-85.
4. D. Bród, On Some Combinatorial Properties of Balancing Split Quaternions, Symmetry (2024), 16, 373. https://doi.org/10.3390/sym16030373

Monografie:

1. D. Bród, A. Szynal-Liana, Jacobsthal numbers, Pell numbers, their generalizations and applications, Oficyna Wydawnicza Politechniki Rzeszowskiej, Rzeszów 2023.

Artykuły:

1. G. Bilgici, D. Bród, On r-Jacobsthal and r-Jacobsthal- Lucas numbers, Annales Mathematicae Silesianae 37, no. 1, (2023), 16-31.
2. D. Bród, A. Szynal-Liana, Generalized commutative Jacobsthal quaternions and some matrices, Examples and Counterexamples (2023) 100102, https://doi.org/10.1016/j.exco.2023.100102.
3. A. Kosiorowska, I. Włoch, On the Existence of Independent [j, k]-Dominating Sets in the Generalized Corona of Graphs, Symmetry 2023, 15, 802. https://doi.org/10.3390/sym15040802
4. D. Bród, A. Szynal-Liana, I. Włoch, One-parameter generalization of the bihyperbolic Jacobsthal numbers, Asian-European Journal of Mathematics 16(05), 2350075 (2023). https://doi.org/10.1142/s1793557123500754
5. M. Nunokawa, J. Sokół, L. Trojnar-Spelina, Some results on p-valent functions, Bulletin des Sciences Mathématiques, 185 (2023) 103269, 16 pages.
6. A. Kosiorowska, A. Michalski, I. Włoch, On minimum intersections of certain secondary dominating sets in graphs, Opuscula Mathematica, 43, no. 6 (2023), 813-827.
7. D. Bród, A. Szynal-Liana, On bihypernomials related to balancing and Chebyshev polynomials, Azerbaijan Journal of Mathematics, vol. 13, no 2 (2023), 200-218.
8. D. Bród, A. Szynal-Liana, I. Włoch, One-parameter generalization of dual-hyperbolic Jacobsthal numbers, Annales Mathematicae Silesianae 37, no. 2, (2023), 224-239.
9. D. Bród, A. Szynal-Liana, A new hybrid generalization of Fibonacci and Fibonacci-Narayana polynomials, Annales UMCS, sectio A, vol. LXXVII, no. 1 (2023), 1-12 doi: 10.17951/a.2023.77.1.1-12.
10. I. Włoch, N. Paja, A. Szynal-Liana, On Some Combinatorial Properties of Oresme Hybrationals, Symmetry 2023, 15(11), 1996; https://doi.org/10.3390/sym15111996

Artykuły:

1. A. Szynal-Liana, I. Włoch, M. Liana, On certain bihypernomials related to Pell and Pell-Lucas numbers, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 71, Issue 2 (2022), 422-433.
2. A. Szynal-Liana, I. Włoch, Generalized commutative quaternions of the Fibonacci type, Bol. Soc. Mat. Mex. 28, 1 (2022)
3. D. Bród, A. Szynal-Liana, On a New Generalization of Jacobsthal Hybrid Numbers, Azerbaijan Journal of Mathematics, vol. 12, no 1, (2022), 20-31.
4. D. Bród, A. Szynal-Liana, I. Włoch, One-parameter generalization of dual-hyperbolic Pell numbers, Mathematica Slovaca 72 (2022), No. 2, 527-537.
5. A. Michalski, I. Włoch, M. Dettlaff, M. Lemańska, On proper (1,2)-dominating sets, Mathematical Methods in the Applied Sciences, 2022;45(11):7050-7057, https://doi.org/10.1002/mma.8223
6. M. Liana, A. Szynal-Liana, I. Włoch, Jacobsthal representation hybrinomials, Annales Mathematicae Silesianae 36 (2022), no. 1, 57–70.
7. P. Bednarz, Relations between the existence of a (2-d)-kernel and parameters γ₂(G), α(G), Indian Journal of Mathematics, Vol. 64, No. 1, (2022), 93-107
8. D. Bród, A. Szynal-Liana, I. Włoch, Two-parameter generalization of bihyperbolic Jacobsthal numbers, Proyecciones Journal of Mathematics, Vol. 41, No 3 (2022), 569-578.
9. A. Włoch, M. Wołowiec-Musiał, U. Bednarz, New Types of Distance Padovan Sequences via Decomposition Technique, Applied Sciences 2022, 12(18), 9163; https://doi.org/10.3390/app12189163
10. A. Szynal-Liana, I. Włoch, A study on Fibonacci and Lucas bihypernomials, Discussiones Mathematicae - General Algebra and Applications 42(2) (2022), 409–423, https://doi.org/10.7151/dmgaa.1399
11. D. Bród, A. Michalski, On generalized Jacobsthal and Jacobsthal-Lucas numbers, Annales Mathematicae Silesianae 36 (2022), no. 2, 115–128. DOI: https://doi.org/10.2478/amsil-2022-0011
12. D. Bród, A. Szynal-Liana, I. Włoch, On some combinatorial properties of generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions, Czechoslovak Mathematical Journal, 72 (147) (2022), 1239–1248
13. V. Polishchuk, M. Kelemen, I. Włoch, O. Tymoshenko, Y. Mlavets, The hybrid mathematical model for the evaluation and selection of iron ore raw materials in the context of the European Green Deal, Acta Montanistica Slovaca, Volume 27 (3), DOI: https://doi.org/10.46544/AMS.v27i3.01
14. D. Bród, A. Szynal-Liana, I. Włoch, Two generalizations of dual-complex Lucas-balancing numbers, Acta Univ. Sapientiae Mathematica 14,2 (2022), 220-230.
15. A. Szynal-Liana, I. Włoch, M. Liana, Generalized commutative quaternion polynomials of the Fibonacci type, Annales UMCS, sectio A, Vol 76, No 2 (2022), 33-44.

Skrypt:

1. A.Szynal-Liana, I.Włoch, Dziesięć wykładów z teorii kwaternionów, Oficyna Wydawnicza PRz, Rzeszów 2022.

1. N. Bednarz, On (k,p)-Fibonacci numbers, Mathematics 2021, 9(7), 727.
2. P. Bednarz, On (2-d)-kernels in the tensor product of graphs, Symmetry, 2021, 13(2), 230.
3. P. Bednarz, N. Paja, On (2-d)-kernels in two generalizations of the Petersen graph , Symmetry, 2021, 13(10), 1948.
4. U. Bednarz, M. Wołowiec-Musiał, Distance Fibonacci Polynomials—Part II, Symmetry, 2021, 13(9), 1723.
5. U. Bednarz, I. Włoch, Fibonacci numbers in graphs with strong (1,1,2)-kernels, Bol. Soc. Mat. Mex. 27, 12 (2021).
6. D. Bród, On balancing and Lucas-balancing quaternions, Discussiones Mathematicae General Algebra and Applications 41(1), (2021), 55-68.
7. D. Bród, On trees with unique locating kernels, Boletín de la Sociedad Matemática Mexicana 27:61 (2021), 1-13.
8. D. Bród, A. Włoch, (2,k)-Distance Fibonacci Polynomials, Symmetry, 2021, 13(2), 303, pages 1-10.
9. D. Bród, A. Szynal-Liana, I. Włoch, Balancing hybrid numbers, their properties and some identities, Indian Journal of Mathematics, vol. 63, no. 1 (2021), 143-157.
10. D. Bród, A. Szynal-Liana, I. Włoch, On a new two-parameter generalization of dual-hyperbolic Jacobsthal numbers, Annales UMCS, sectio A, Vol 75, No 1 (2021), 1-14.
11. D. Bród, A. Szynal-Liana, I. Włoch, On some combinatorial properties of bihyperbolic numbers of the Fibonacci type, Mathematical Methods in the Applied Sciences 2021; 44: 4607-4615.
12. D. Bród, A. Szynal-Liana, I. Włoch, On a new generalization of bihyperbolic Pell numbers, Annals of the “Alexandru Ioan Cuza” University of Iaşi (New Series). Mathematics, LXVII, f.2, (2021), 251-260.
13. D. Bród, A. Szynal-Liana, I. Włoch, On a new one-parameter generalization of dual-complex Jacobsthal numbers, Acta Univ. Sapientiae, Mathematica, 13, 1 (2021) 127-144.
14. R. Kargar, L. Trojnar-Spelina, Starlike functions associated with the generalized Koebe function, Analysis and Mathematical Physics, Volume 11, Issue 4, 2021.
15. N. Paja, I. Włoch, Some interpretations of the (k; p)-Fibonacci numbers, Commentationes Mathematicae Universitatis Carolinae, 62,3 (2021) 297-307.
16. V. Polishchuk, M. Kelemen, I. Włoch, A. Polishchuk, M. Sharkadi, Yu. Mlavets, Conceptual Model of Presentation of Fuzzy Knowledge. CEUR Workshop Proceedings, Vol.3018, 2021 – P.1-12.
17. A. Michalski, P. Bednarz, On independent secondary dominating sets in generalized graph products, Symmetry, 2021, 13(12), 2399.
18. D. Bród, A. Szynal-Liana, I. Włoch, Bihyperbolic numbers of the Fibonacci type and their idempotent representation, Commentationes Mathematicae Universitatis Carolinae, 62,4 (2021) 409-416.

1. D. Bród, On a new Jacobsthal-type sequence, Ars Combinatoria 150, 2020, 21-29
2. D. Bród, On distance (k,t)-Fibonacci numbers and their applications,Ars Combinatoria 152 (2020), 129-139.
3. A. Michalski, I. Włoch, On the existence and the number of independent (1,2)-dominating sets in the G-join of graphs, Applied Mathematics and Computation 377 (2020) 125155; DOI: 10.1016/j.amc.2020.125155
4. U. Bednarz, Strong (1;1;2)-kernels in the corona of graphs and some realization problems, Iranian Journal of Science and Technology, Transactions A: Science (2020), DOI : 10.1007/s40995-020-00830-6
5. U. Bednarz, M. Wołowiec-Musiał, Distance Fibonacci Polynomials, Symmetry 2020, 12(9), 1540, pages 1-14
6. U. Bednarz, I. Włoch, On strong (1,1,2)-kernels in graphs, Ars Combinatoria, 152, 32-43, 2020.
7. A. Szynal-Liana, I. Włoch, Generalized Fibonacci-Pell hybrinomials, Online Journal of Analytic Combinatorics, Issue 15 (2020), #14, 1-12
8. A. Szynal-Liana, I. Włoch, Introduction to Fibonacci and Lucas hybrinomials, Complex Variables and Elliptic Equations vol. 65, no. 10 (2020), 1736-1747
9. A. Szynal-Liana, I. Włoch, On generalized Mersenne hybrid numbers, Annales UMCS, sectio A, vol. LXXIV, no. 1 (2020), 77-84
10. A. Szynal-Liana, I. Włoch, On Special Spacelike Hybrid Numbers, Mathematics 2020, 8(10), 1671, 1-10
11. A. Szynal-Liana, I. Włoch, M. Liana, Some identities for generalized Fibonacci and Lucas numbers, AKCE International Journal of Graphs and Combinatorics, vol. 17, no. 1 (2020), 324-328
12. M. Nunokawa, J. Sokół, L. Trojnar-Spelina, On a sufficient condition for function to be p-valent close-to-convex, The Ramanujan Journal, 53, 483-492 (2020)
13. D. Bród, On split r-Jacobsthal quaternions, Annales UMCS, sectio A, vol. LXXIV, no. 1 (2020), 1-14
14. D. Bród, On some properties of split Horadam quaternions, Acta Univ. Sapientiae, Mathematica 12, 2 (2020), 260-271.
15. D. Bród, A. Szynal-Liana, On J(r,n)-Jacobsthal hybrid numbers, Tatra Mountains Mathematical Publications, 77 (2020), 13-26
16. D. Bród, A. Szynal-Liana, On some combinatorial properties of P(r,n)-Pell quaternions, Tatra Mountains Mathematical Publications, 77 (2020), 1-12
17. D. Bród, A. Szynal-Liana, I. Włoch, On the combinatorial properties of bihyperbolic balancing numbers, Tatra Mountains Mathematical Publications, 77 (2020), 27-38
18. D. Bród, A. Szynal-Liana, I. Włoch, Two generalizations of dual-hyperbolic balancing numbers, Symmetry 2020, 12(11), 1866, 1-11
19. A. Włoch, I. Włoch, On some multinomial sums related to the Fibonacci type numbers, Tatra Mountains Mathematical Publications, 77 (2020), 99-108

Monografie:

1. A. Szynal-Liana, I. Włoch, Hypercomplex numbers of the Fibonacci type, Oficyna Wydawnicza Politechniki Rzeszowskiej, Rzeszów, 2019.

Artykuły:

1. L. Trojnar-Spelina, I. Włoch, On Generalized Pell and Pell-Lucas Numbers, Iranian Journal of Science and Technology, Transactions A: Science, December 2019, Volume 43, Issue 6, pp 2871-2877.
2. L. Trojnar-Spelina, I. Włoch, On new types of the companion Pell numbers, Ars Combinatoria 142 (2019), 221-230.
3. A. Szynal-Liana, I. Włoch, The Fibonacci Hybrid numbers, Utilitas Mathematica 110 (2019), 3-10.
4. R. Kargar, A. Ebadian, L. Trojnar-Spelina, Further results for starlike functions related with Booth lemniscate, Iranian Journal of Science and Technology, Transactions A: Science 43 (3)(2019), 1235-1238.
5. U. Bednarz, M. Wołowiec-Musiał, On a new generalization of telephone numbers, Turkish Journal of Mathematics 43 (2019), 1595-1603.
6. D. Bród, On a new one parameter generalization of Pell numbers, Annales Mathematicae Silesianae 33 (2019), 66-76.
7. A. Szynal-Liana, I. Włoch, On Jacobsthal and Jacobsthal-Lucas Hybrid Numbers, Annales Mathematicae Silesianae 33 (2019), 276-283.
8. R. Kargar, L. Trojnar-Spelina, Some applications of differential subordination for certain starlike functions, Turkish Journal of Mathematics 43 (2019), 1988-1999.
9. D. Bród, On a new generalization of split Pell quaternions, Mathematica Applicanda 47(2) (2019), 245-258.
10. M. Liana, A. Szynal-Liana, I. Włoch, On Pell hybrinomials, Miskolc Mathematical Notes Vol. 20 (2019), No. 2, pp. 1051-1062.
11. D. Bród, A. Szynal-Liana, On a new generalization of Jacobsthal quaternions and several identities involving these numbers, Commentationes Mathematicae, vol. 1-2, no. 59 (2019), 33-45.
12. M. Liana, A. Szynal-Liana, I. Włoch, On some kind of numbers of the Fibonacci type and their applications for bicomplex numbers, Bulletin de la Societe des Sciences et des Lettres de Łódź, vol. LXIX, no. 1 (2019), 129–138.

1. A. Szynal-Liana, I. Włoch, On F(p,n)-Fibonacci Quaternions, Bulletin de la Societe des Sciences et des Lettres de Łódź, vol. LXVIII, no. 1 (2018), 131-140.
2. N. Bednarz, A. Włoch, I. Włoch, The Fibonacci numbers in edge coloured unicyclic graphs, Utilitas Mathematica 106 (2018), 39-49.
3. U. Bednarz, I. Włoch, Fibonacci and telephone numbers in extremal trees, Discussiones Mathematicae Graph Theory 28 (2018), 121-133.
4. J. Brzdęk, E. Jabłońska, J. Olko, On approximate roots of polynomials and systems of polynomials in ultrametric Banach algebras, J. Math. Anal. Appl. 464 (2018), 531-545.
5. R. Kargar, J. Sokół, A. Ebadian, L. Trojnar-Spelina, On a class of starlike functions related with Booth lemniscate, Proceedings of Jangjeon Mathematical Society 21 (2018)(3), 479-486.
6. K. Piejko, L. Trojnar-Spelina, On (A,2B,2C)-edge colourings in certain class of graphs, Ars Combinatoria 139 (2018), 119-131.
7. A. Szynal-Liana, The Horadam Hybrid Numbers, Discussiones Mathematicae - General Algebra and Applications 38 (2018), 91-98.
8. D. Bród, On a two-parameter generalization of Jacobsthal numbers and its graph interpretation, Annales UMCS, sectio A, vol. LXXII, no.2 (2018), 21-28.
9. A. Szynal-Liana, I. Włoch, On Pell and Pell-Lucas Hybrid Numbers, Commentationes Mathematicae, vol.56, no 1-2 (2018), 11-17.
10. M. Liana, A. Szynal-Liana, I. Włoch, On F(p,n)-Fibonacci bicomplex numbers, Scientific Issues of Jan Długosz University in Czestochowa, Mathematics XXIII (2018), 35-44
11. M. Nunokawa, J. Sokół, L. Trojnar-Spelina, On some conditions for p-valency, Filomat 32(17)(2018), 6107-6114.
12. D. Bród, A. Szynal-Liana, On J(r,n)-Jacobsthal Quaternions, Pure and Applied Mathematics Quarterly, vol.14, no. 3-4 (2018), 579-590.

1. P. Bednarz, I. Włoch, An algorithm determining (2-d)-kernels in trees, Utilitas Mathematica 102 (2017), 215-222.
2. U. Bednarz, D. Bród, A. Szynal-Liana, I. Włoch, M. Wołowiec-Musiał, On Fibonacci numbers in edge coloured trees, Opuscula Math. 37, no. 4 (2017), 479-490.
3. U. Bednarz, I. Włoch, Note about sequences of extremal (A,2B)-edge coloured trees, Annales UMCS, sec. A Vol LXXI No 2 (2017), 17-23.
4. D. Bród, On two-parameters generalization of Fibonacci numbers, Mathematica Applicanda, Vol. 45(1), (2017), p.81–92.
5. J. Brzdęk, E. Jabłońska, On extensions of the generalized Jensen functions on semigroups, Bull. Aust. Math. Soc. 96 (1) (2017), 110-116.
6. E. Jabłońska, Remarks on analogies between Haar meager sets and Haar null sets, rozdział w monografii: Developments in Functional Equations and Related Topic pod redakcją J. Brzdęka, K. Cieplińskiego i Th.M. Rassiasa, Springer Optimization and its Applications 124, Springer, (2017), 149-159.
7. A. Szynal-Liana, I. Włoch, Some properties of generalized Tribonacci quaternions, Scientific Issues of Jan Długosz University in Czestochowa, Mathematics XXII (2017), 73–81.
8. A. Włoch, M. Wołowiec-Musiał, On generalized telephone numbers, their interpretations and matrix generators, Utilitas Mathematica 105 (2017), 31-39.

1. A. Bahyrycz, J. Brzdęk, E. Jabłońska, On extensions of the generalized cosine functions from some large sets, Publ. Math. Debrecen 89/3 (2016), 263-275.
2. A. Bahyrycz, J. Brzdęk, E. Jabłońska, R. Malejki, Ulam's stability of a generalization of the Frechet functional equation, J. Math. Anal. Appl. 442 (2) (2016), 537-553.
3. P. Bednarz, I Włoch, On (2-d)-kernels in the cartesian product of graphs, Ann. Univ. Mariae Curie-Skłodowska Sect. A, 70 (2) (2016), 1-8.
4. U. Bednarz, M. Wołowiec-Musiał, Two-parameters generalization of Pell numbers in graphs, Ars Combinatoria 129 (2016), 19-31.
5. D. Bród, P. Rachwał, P. Strzelecki, Projekcja odwrócona (inverse projection)jako narzędzie wspomagające poznanie przeszłości demograficznej, Przeszłość Demograficzna Polski 38, nr 4,(2016),89-117.
6. J. Brzdęk, E. Jabłońska, M.S. Moslehian, P. Pacho, On stability of a functional equation of quadratic type, Acta Math. Hungar. 149 (2016), 160-169.
7. E. Jabłońska, A theorem of Piccard's type and its applications to polynomial functions and convex functions of higher orders, Topology Appl. 209 (2016), 46-55.
8. E. Jabłońska, A theorem of Piccard's type in abelian Polish groups, Anal. Math. 42 (2016), 159-164.
9. E. Jabłońska, D-measurability and t-Wright convex functions, J. Math. Inequal. 10 (2016), 213-217.
10. A. Szynal-Liana, I. Włoch, A note on Jacobsthal quaternions, Advances in Applied Clifford Algebras 26 (2016), 441-447.
11. A. Szynal-Liana, I. Włoch, The Pell quaternions and the Pell octonions, Advances in Applied Clifford Algebras 26 (2016), 435-440.
12. L. Trojnar-Spelina, I. Włoch, On Pell numbers and (k1A1,k2A2,k3A3)-edge colouring in graphs, Ars Combinatoria 125 (2016), 183-191.