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Details of project

  
Identifier
49433
Type K
Principal investigator Czédli, Gábor
Title in Hungarian Hálók és más algebrák
Title in English Lattices and other algebras
Panel Mathematics and Computing Science
Department or equivalent Bolyai Institute (University of Szeged)
Participants Katonáné Dr. Horváth, Eszter
Radeleczki, Sándor
Schmidt, Tamás
Starting date 2005-01-01
Closing date 2009-12-31
Funding (in million HUF) 7.742
FTE (full time equivalent) 3.48
state closed project





 

Final report

  
Results in Hungarian
A tervezett 10 cikk helyett megjelent 15, megjelenés alatt áll 6, és további 8 be van nyújtva. A fő eredmények az alábbiak. Jelöljön F féligmoduláris, D pedig véges disztributív hálót. Ha F véges hosszúságú, akkor fedésőrzően ekvivalenciahálóba ágyazható be [19]. Új struktúratételünk: ha F véges, akkor alkalmas D-ből nyerhető [8]. Fordítva, D pedig egy majdnem geometriai F kongruenciahálójával izomorf [21]. Több tétel jelzi, hogy beindult a fraktálhálók kutatása [4, 5]. Hálók kombinatorikai vonatkozásai terén eredmények születtek a Frankl-sejtésről [9, 11, 15], a CD és CDW bázisokról [13, 14], valamint a sziget számáról [6, 28, 29]. Az involúciós hálókra nyert eredményeknek kísérőhálókra vonatkozó következménye is van [26]. A 2-uniform kongruenciák felcserélhetőségének kutatása [1, 3] egy új lezárási operátorhoz vezetett [7, 10, 17].
Results in English
Instead of the planned 10 research papers, 15 have appeared, 6 are accepted and 8 are submitted. The main results are as follows. Let F resp. D denote a semimodular resp. finite distributive lattice. If F is of finite length, then it has a cover-preserving embedding into an equivalence lattice [19]. Our new structure theorem states that if F is finite, then it is derived from a suitable D [8]. In the other direction, D is isomorphic to the congruence lattice of an almost geometric F [21]. Several theorems indicate the start of studying fractal lattices [4, 5]. Belonging to the combinatorial aspects of lattice theory, results on Frankl’s conjecture [9, 11, 15], CD and CDW bases [13, 14], and the number of islands [6, 28, 29] have been achieved. New results on involution lattices were proved and applied to related lattices [26]. The study of permutability of 2-uniform congruences [1, 3] led to a new closure operator [7, 10, 17].
Full text http://real.mtak.hu/1975/
Decision
Yes





 

List of publications

  
[24] I. Chajda and S. Radeleczki: Semilattices with sectionally antitone bijections, Novi Sad J. Math. Vol. 35, No 1, 93 - 101, 2005
[22] Attila Körei and Sándor Radeleczki: Box elements in a concept lattice, ICFCA06 Conference Dresden, Conference Suplement, pp. 97-109. Editors: B. Ganter and L. Kwuida. Verlag. Allgemeine Wissenschaft, Drezda, 2006
[6] G. Czédli:: The number of rectangular islands by means of distributive lattices, European Journal of Combinatorics 30 (2009), 208-215., 2009
[10] G. Czédli: A fixed point theorem for stronger association rules and its computational aspects, Acta Cybernetica, to appear, 2009
[11] G. Czédli and E. T. Schmidt: Frankl's conjecture for large semimodular and planar semimodular lattices, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 47 (2008), 47-53., 2008
[12] G. Czédli: A visual approach to test lattices, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica, to appear., 2009
[13] G. Czédli and E. T. Schmidt: CDW-independent subsets in distributive lattices, Acta Sci. Math. (Szeged), to appear., 2009
[14] G. Czédli, M. Hartmann and E.T. Schmidt: CD-independent subsets in distributive lattices, Publicationes Mathematicae Debrecen, 74/1-2 (2009), 127-134., 2009
[16] G. Czédli and M. Maróti: Two notes on the variety generated by planar modular lattices, Order, to appear., 2008
[17] G. Czédli: A stronger association rule in lattices, posets and databases, Order, submitted, 2010
[18] G. Czédli, M. Erné, B. Seselja and A. Tepavcevic: Characteristic triangles of closure operators with applications in general algebra, Algebra Universalis, submitted., 2010
[19] G. Czédli and E. T. Schmidt: A cover-preserving embedding of semimodular lattices into geometric lattices, Advances in Mathematics, submitted., 2010
[20] G. Czédli and M. Maróti: On the height of order ideals, Mathematica Bohemica, submitted., 2010
[21] G. Czédli and E. T. Schmidt: Finite distributive lattices are congruence lattices of almost-geometric lattices, Algebra Universalis, submitted., 2010
[23] I. Chajda and S. Radeleczki: On congruences of algebras defined on sectionally pseudocomplemented lattices, Proceedings of the 6-th International Conference on Algebra and Model Theory, Novosibirsk, August 2006. pp. 8-23., 2005
[26] R. Pöschel and S. Radeleczki: Related structures with involution, Acta Math. Hungarica, to appear, 2009
[27] J. Järvinen, S. Radeleczki and L. Veres: Rough sets determined by quasiorders, Order, submitted, 2010
[28] E. K. Horváth, Z. Németh, G. Pluhár: The number of triangular islands on a triangular grid, Periodica Mathematica Hungarica, to appear, 2010
[29] E. K. Horváth, G. Horváth, Z. Németh, Cs. Szabó: The number of square islands on a rectangular sea, Acta Sci. Math., submitted, 2010
[1] G. Czédli:: 2-uniform congruences in majority algebras and a closure operator, Algebra Universalis, 57 (2007), 63-73., 2007
[2] G. Czédli, B. Seselja and A. Tepavcevic: On the semidistributivity of elements in weak congruence lattices of algebras and groups, Algebra Universalis 58 (2008) 349-355, 2008
[3] G. Czédli:: Idempotent Mal'cev conditions and 2-uniform congruences, Algebra Universalis 59 (2008) 303-309, 2008
[4] G. Czédli:: Some varieties and convexities generated by fractal lattices, Algebra Universalis, 60 (2009), 107-124., 2009
[5] G. Czédli:: The product of von Neumann n-frames, its characteristic, and modular fractal lattices, Algebra Universalis, published online (February 10, 2009), DOI: 10.1007/s00012-009-2107-3, 2009
[7] G. Czédli:: Stronger association rules for positive attributes, Novi Sad Journal of Mathematics 38 (2008), 103-110., 2008
[8] G. Czédli and E.T. Schmidt: How to derive finite semimodular lattices from distributive lattices?, Acta Mathematica Hungarica, 121/3 (2008) 277-282., 2008
[9] G. Czédli: On averaging Frankl's conjecture for large union-closed sets, Journal of Combinatorial Theory - Series A, 116 (2009), 724-729., 2009
[15] G. Czédli, M. Maróti and E. T. Schmidt: On the scope of averaging for Frankl's conjecture, Order, to appear., 2009
[25] Pöschel, R. and Radeleczki, S.: Endomorphisms of quasiorders and related lattices, Contributions to General Algebra, 18 (2008), 113 - 128., 2008



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