Problematyka badawcza

1. Kombinatoryka algebraiczna. Złożoność obliczeniowa algorytmów.

2. Spektralna analiza Coxetera grafów krawędziowo dwudzielnych (w skrócie: bigrafów, ang. edge-bipartite graphs), algebr, koalgebr oraz zbiorów częściowo uporządkowanych.

3. Numeryczne i graficzne algorytmy klasyfikacyjne dla grafów krawędziowo dwudzielnych z nieujemnym funkcjonałem zysku.

4. Metody kombinatoryczno-algorytmicznej teorii grup, teorii reprezentacji i kategoryjnych problemów macierzowych.

5. Kombinatoryka i struktura grup Coxetera-Weyla bigrafów oraz sieciowe geometrie orbit w systemach pierwiastków.

6. Matematyka konstruktywna, obliczalność, obliczenia symboliczne.

7. Algorytmy toroidalno-sieciowe w spektralnej analizie Coxetera oraz elementarnej geometrii diofantycznej.

Publikacje związane z problematyką badawczą

1. R. Bocian, M. Felisiak, and D. Simson, Numeric and mesh algorithms for the Coxeter spectral study of positive edge-bipartite graphs and their isotropy groups, J. Comput. and Applied Math. 2013, published online 31 July 2013, doi: 10.1016.cam.2013.07.013.
2. R. Bocian, M. Felisiak and D. Simson, On Coxeter type classification of loop-free edge-bipartite graphs and matrix morsifications, SYNASC13, IEEE CPS, Tokyo, 2013.
3. P. Dowbor, H. Meltzer and A. Mróz, An algorithm for the construction of exceptional modules over tubular canonical algebras, J. Al gebra 323 (2010), 2719-2734.
4. P. Dowbor, H. Meltzer and A. Mróz, An algorithm for the construction of parametrizing bimodules for homogeneous modules over tubular canonical algebras, Algebras and Repr. Theory , online 27 June 2013, 1–49, doi: 10.1007/s10468-013-9430-2.2012.16.
5. M. Felisiak and D. Simson, Experiences in computing mesh root systems for Dynkin diagrams using Maple and C++, SYNASC11, IEEE Computer Society, Tokyo, 2011, 83–86, doi: 10.1109/SY-NASC.2011.41.
6. M. Felisiak and D. Simson, On computing mesh root systems and the isotropy group for simply-laced Dynkin diagrams, SYNASC12, IEEE Computer Society, Tokyo, 2012, 91-97, doi: 10.1109/SY-NASC.2012.16.
7. M. Felisiak, Computer algebra technique for Coxeter spectral study of edge-bipartite graphs and matrix morsifications of Dynkin type A n , Fund. Inform . 125 (2013), 21–49, doi: 10.3233/FI-2013-851.
8. M. Felisiak and D. Simson, On combinatorial algorithms computing mesh root systems and ma-trix morsifications for the Dynkin diagram A n , Discrete Math. 313 (2013), 1358–1367, doi: 10.1016/j.disc.2013.02.003.
9. M. Gasiorek, Efficient computation of the isotropy group of a finite graph: a combinatorial ap-proach, SYNASC13, IEEE Computer Society, Tokyo, 2013.
10. M. Gąsiorek and D. Simson, One-peak posets with positive Tits quadratic form and their mesh translation quivers of roots, and programming in Maple and Python, Linear A lgebra and Appl. 436(2012), pp. 2240–2272, doi: 10.1016/j.laa. 2011.10.045.
11. M. Gąsiorek and D. Simson, A computation of positive one-peak posets that are Tits sincere, Collo q. Math . 127 (2012), 83–103, doi:10.4064/cm127-1-6.
12. M. Gąsiorek and D. Simson, A classification of positive posets using isotropy groups of Dynkin diagrams, EuroComb 2013 , in: Centro di Riserca Matematica Series (Edicioni della Normale, Scuola Normale Superiore Pisa), Vol 16, 2013, pp. 599–605.
13. M. Gąsiorek, D. Simson, and K. Zaj¸ac, On Coxeter spectral study of posets and a digraph iso-morphism problem, SYNASC12, IEEE Computer Society, Tokyo, 2012, pp. 369-375.
14. M. Gąsiorek, D. Simson and K. Zając, Algorithmic computation of principal posets using Maple and Python, Algebra and Discr. Math. 17 (2014), 1-28.
15. S. Kasjan and A. Mróz, Tree matrices and matrix reduction algorithm of Belitskii, Europ. J. Combin. Fund. Inform. 118(2012), 253-279, współautor M. Grzecza.
16. S. Kasjan and A. Mróz, Experiences in symbolic computations for matrix problems, SYNASC12, IEEE Computer Society, Tokyo, 2012, pp. 39-44.
17. J. Kosakowska, Inflation algorithms for positive and principal edge-bipartite graphs and unit quadratic forms, Fund. Inform . 119 (2012), 149-162.
18. W. Kraśkiewicz, Schubert functors and Schubert polynomials, Europ. J. Combin. 25 (2004), 1327–1344, współautor P. Pragacz.
19. W. Kraśkiewicz, Covariants of spherical Θ-orbits for types E 6 , E 7 , E 8 , EuroComb 2013 , in: Centro di Riserca Matematica Series (Edicioni della Normale, Scuola Normale Superiore Pisa), Vol 16, 2013, pp. 401–406, współautor J. Weyman.
20. P. Krysztowiak, An improved approximation ratio for the jump number problem on iterval orders, Theoret. Comp. Sci. 2013, w druku, dx.doi.org/10.1016/tcs2013.10.011.
Zakład Kombinatoryki 3
21. A. Mróz, On the computational complexity of Bongartzs algorithm, Fund. Inform. 123 (2012), 317-329.
22. G. Marczak, A. Polak and D. Simson, P -critical integral quadratic forms and positive forms. An algorithmic approach, Linear Algebra Appl. 433 (2010), pp. 1873–1888, doi: 10.1016/j.laa. 2010.06.052.
23. G. Marczak, D. Simson and K. Zając, On computing non-negative loop-free edge-bipartite graphs, SYNASC13, IEEE Computer Society, Tokyo, 2013.
24. A. Polak and D. Simson, Algorithmic experiences in Coxeter spectral study of P-critical edge-bipartite graphs and posets, SYNASC13, IEEE Computer Society, Tokyo, 2013.
25. A. Polak and D. Simson, Algorithms computing O(n, Z )-orbits of P -critical edge-bipartite graphs and P -critical unit forms by using Maple and C#, Algebra and Discrete Math. 16(2013), No.2, 1-32.
26. D. Simson, Integral bilinear forms, Coxeter transformations and Coxeter polynomials of finite posets, Linear Algebra Appl. , 433 (2010), 699–717; doi: 10.1016.laa.2010.03.041.
27. D. Simson, Mesh algorithms for solving principal Diophantine equations, sand-glass tubes and tori of roots, Fund. Inform. 109 (2011), 425-462.
28. D. Simson, Algorithms determining matrix morsifications, Weyl orbits, Coxeter polynomials and mesh geometries of roots for Dynkin diagrams, Fund. Inform. 123 (2013), 447-490, doi: 10.3233I-2013-820.
29. D. Simson, A Coxeter-Gram classification of positive simply-laced edge-bipartite graphs, SIAM J. Dis cret e Math. 27 (2013), 827–854, doi: 10.113710843721.
30. D. Simson, A framework for Coxeter spectral analysis of edge-bipartite graphs, their rational morsifications and mesh geometries of root orbits, Fund. Inform . 124 (2013), 309-338.
31. D. Simson, Toroidal algorithms for mesh geometries of root orbits of the Dynkin diagram D 4, Fund. Inform . 124 (2013), 339-364.
32. D. Simson and K. Zając, A framework for Coxeter spectral classification of finite posets and their mesh geometries of roots, International J. Math. Math. Sciences , Volume 2013, Article ID 743734, 22 pages, http./dx.doi.org/10.1155/2013/743734.

Skład osobowy

Zakład Kombinatoryki i Obliczeń Symbolicznych


kierownik: prof. dr hab. Daniel Simson

dr hab. Grzegorz Jarzembski, prof. UMK
dr hab. Justyna Kosakowska, prof. UMK
dr Rafał Bocian
dr Witold Kraśkiewicz
dr Andrzej Kurpiel
dr Andrzej Mróz
mgr Marcin Gąsiorek
mgr Katarzyna Zając

Doktoranci

  •   mgr Mariusz Felisiak
  •   mgr Marcin Gąsiorek
  •   mgr Katarzyna Zając