Research


  • Subject of My Research
     

 My research interests concern applications of probabilistic methods to asymptotic enumeration problems of combinatorics and graph theory. The results obtained are usually given in the form of probabilistic limit theorems of local and integral type. Thus, a concrete class of combinatorial structures is always studied in the context of a probability space. The latter has been previously provided with an appropriate probability measure defined on the class under consideration.
     A significant part of the results in my publications is devoted to models of random mappings of a finite set into itself. The uniform model, the model with a single attracting center the general (T; Pj) model as well as random permutations and random mapping patterns are studied. Various asymptotic results are obtained under the assumption that the cardinality of the underlying set tends to infinity.
    Combinatorial structures which posses generating functions satisfying wild analytical conditions of admissibility type are also investigated. This approach enables us to obtain some asymptotic properties of other types of structures: random partitions of a finite set and random partitions of a positive integer.
 

  • Research Work in Progress

 

At present I am interested in:
 

    • establishing local limit theorems for sums of i.i.d. discrete random variables when their distribution depends on the number of summands;
    • applying such results to the asymptotic enumeration of various kinds of combinatorial structures (mappings, trees, forests, partitions);
    • applying results of random mapping theory to network models and especially to models of a contagious disease spread along the arcs of certain types of random graphs;

  • Teaching Experience
    • Lectures and Seminars:

Statistics and Business Statistics (required courses for the students in the American University in Bulgaria)
Mathematical Statistics (a Mathematics Major course for the students in the American University in Bulgaria)
Statistical Methods in Research (a Mathematics Major course for the students in the American University in Bulgaria)
Combinatorial Analysis and Probabilities (a course for graduate students in mathematical statistics, lectured in 1978, 1983, 1985 and 1989 at
Sofia University)
Mathematical Statistics for Biologists (a course, lectured in the period 1978-88 at Sofia University)

 

    • Supervising PhD, Graduate and Undergraduate Students.

Sofia University: Diploma works defended at the Faculty of Mathematics and Informatics of Sofia University in 1979, 1981, 1991, and 1998.

Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences: PhD student: Emil Kamenov; thesis defended in May, 2012.

American University in Bulgaria: Senior Theses defended in 2008 and 2011.

 

 


  • Recent Publications

 

  1. Mutafchiev, L., On the size of the Durfee square in a random integer partition, J. Comput. Appl. Math. 142 (2002), 173-184.    
        (PDF version here)
  2. Mutafchiev, L., The typical growth of the kth excess in a random integer partition, Monatsh. Math 136 (2002), 313-325.
        (PDF version here)
  3. Mutafchiev, L., Erratum, J. Combinatorial Theory, Series A 102 (2003), 447-449
        (PDF version here)
  4.  Kolev, N. and Mutafchiev, L., A zero-inflated occupancy distribution: exact results and Poisson convergence, Int. J. Math. & Math. Sci., 203(2003), 1771-1782.
        (PDF version here)
  5.   Mutafchiev, L., On the Maximal Multiplicity of Parts in a Random Integer Partition, The Ramanujan Journal. 9(2005), 305-316..
        (PDF version here)
  6. Yanev, G. P. and Mutafchiev, L., Number of Complete N-ary subtrees on Galton-Watson Family Trees, Methodology and Computing in Applied Probability, 8 (2006), 223-233, Available at: http://arxiv.org/abs/math.PR/0601585
  7. Mutafchiev, L., The Size of the Largest Part of Random Plane Partitions of Large Integers, INTEGERS: Electron Journal of Combinatorial Number Theory, 6 (2006), #A13. Available at: http://www.integers-ejcnt.org/vol6.html 
  8. Mutafchiev, L., Kamenov E., Asymptotic Formula for the Number of Plane Partitions of Positive Integers, Compt. Rend. Acad. Bulg. Sci., 59 (2006), No 4, 361-366.
        (PDF version here)
  9. Mutafchiev, L., Asymptotic Enumeration of Plane Partitions of Large Integers and Haymanís Theorem for Admissible Generating Functions.
        (PDF version here)
  10. Mutafchiev, L., Kamenov E., The Limiting Distribution of the Trace of a Random Plane Partition. Acta Math Hungar., 117 (4) (2007), 293-314. Available athttp://arxiv.org/abs/math/0411377.

11.  Mutafchiev, L., Survival Probabilities for N-ary Subtrees on a Galton-Watson Family Tree. Statistics & Probability Letters 78 (2008) 2165-2170. Available at††† http://arxiv.org/abs/0706.1904

12.  Mutafchiev, L., Limit theorems for the number of parts in a random weighted partition. The Electronic Journal of Combinatorics 18(1), P206. Available at http://www.combinatorics.org/Volume_18/PDF/v18ilp206.pdf

13.  Mutafchiev, L., The size of the largest part of random weighted partitions of large integers. Combinatorics, Probability and Computing 22(2013), 433-454. Available at http://arxiv.org/abs/1107.4754

14.  Mutafchiev, L., Sampling part sizes of random integer partitions. Ramanujan J. DOI 10.1007/s11139-014-9559-6 Available at http://arxiv.org/abs/1306.6155v2

15.  Mutafchiev, L., A note on Goldbach Partitions Of Large Even Integer. Electronic J. Comb. 22(1) (2015), #P1.40 (Available on the website of the journal).

  1. Mutafchiev, L., Sampling parts of random integer partitions: a probabilistic and asymptotic analysis. Pure Mathematics and Applications Vol.25 (2015), No.1, pp.79-95.Available athttp://arxiv.org/pdf/1407.3639.pdf
  2. Mutafchiev, L., On the Distribution of the Number of Goldbach Partitions of a Randomly Chosen Positive Even Integer. Electronic Notes in Discrete Mathematics 54(2016), 3-8. Available at http://arxiv.org/pdf/1602.01232.pdf

 

 

 

 


  • List of Publications
    1. Mutafchiev, L., Cycles in random permutations of a symmetric groups of high order, Math. Balkanica (Belgrade) 6 (1976), 133-148.
    2. Mutafchiev, L., Limit properties of components of random mappings, C. R. Acad. Bulgare Sci. 31 (1978), 1257-1260.
    3. Mutafchiev, L., Random mappings and their application to epidemic processes, C. R. Acad. Bulgare Sci. 32 (1979), 879-882.
    4. Mutafchiev, L., Limit distributions of some characteristics of components of random mappings, "Mathematics and Mathematical Education" (Sunny Beach 1979), Bulgar. Acad. Nauk, Sofia, 1979, pp. 400-405.
    5. Mutafchiev, L., Epidemic processes on random graphs and their threshold function, Serdica 7 (1981), 153-159.
    6. Mutafchiev, L., A limit distribution related to random mappings and its application to an epidemic process, Serdica 8 (1982), 197-203.
    7. Mutafchiev, L., On some stochastic problems of discrete mathematics, "Mathematics and Mathematical Education" (Sunny Beach 1984), Bulgar. Acad. Nauk, Sofia, 1984, pp. 57-80.
    8. Mutafchiev, L., Limit distributions related to the weight Stirling numbers of the first and second kind, "Limit Theorems in Probability and Statistics", Vol. I, II (Veszprm, Hungary, 1982). Colloq. Math Soc. Janos Bolyai, 36, North Holland, Amsterdam- New York, 1984, pp. 823-842.
    9. Mutafchiev, L., Probability distributions and asymptotics for some characteristics of random mappings, in "Mathematical Statistics and Applications", Vol. B. Proc. of the 4th Pannonian Symp. on Math. Stat., Bad Tatzmannsdorf, Austria, 1983, Reidel, Dordrecht - Boston, Mass. - London, 1985, pp. 227-238.
    10. Mutafchiev, L., A random sampling procedure from a finite population and some applications, Ann. Discr. Math. 28 (1985), 189-197.
    11. Mutafchiev, L., On random mappings with a single attracting centre, J. Appl. Probab. 24 (1987), 258-264.
    12. Mutafchiev, L., The limit distribution of the number of nodes in low strata of a random mapping, Statist. Probab. Letters 7 (1988), 247-251.
    13. Mutafchiev, L., Limit theorems concerning random mapping patterns, Combinatorica 8 (1988), 345-356.
    14. Berg, S. and L. Mutafchiev, Random mappings with an attracting center: Lagrangian distributions and a regression function, J. Appl. Probab. 27 (1990), 622-636.
    15. Mutafchiev, L., Large components and cycles in a random mapping pattern, "Random Graphs' 87. Proc. of the 3rd International Seminar on Random Graphs and Probabilistic Methods in Combinatorics", Poznan, Poland, 1987, John Wiley and Sons Ltd., New York, 1990, pp. 189-202.
    16. Mutafchiev, L., On random mappings of finite sets, "Random Graphs' 89. Proc. of the 4th International Seminar on Random Graphs and Probabilistic Methods in Combinatorics and Computer Science", Poznan, Poland, 1989, John Wiley and Sons Ltd., New York, 1992, pp. 197-214.
    17. Mutafchiev, L., Local limit theorems for sums of power series distributed random variables and for the number of components in labeled relational structures, Random Structures Alg. 3 (1992), 403-426.
    18. Mutafchiev, L., Large trees on a random mapping pattern, Europ. J. Combinatorics 14 (1993), 341-349.
    19. Mutafchiev, L., Random mappings and trees: relations between asymptotics of moments of certain characteristics, "Probabilistic Methods in Discrete Mathematics. Proc of the 3rd Petrozavodsk Conf., Petrozavodsk (Russia), May 11-16, 1992. JVP, Moskva. Prog Pure & Appl. Discr. Math., Vol. 1 (1993), pp. 353-365.
    20. Jaworski, J. and L. Mutafchiev, The largest connected component in a random mapping, Random Structures Alg. 5 (1994), 73-94.
    21. Mutafchiev, L., Local limit approximations for Lagrangian distributions, Aequationes Math. 49 (1995), 57-85.
    22. Baron, G., M. Drmota and L. Mutafchiev, Predecessors in random mappings, Combinatorics Probab. Computing 5 (1996), 317-335.
    23. Mutafchiev, L., Limiting distributions for the number of distinct component sizes in relational structures, J, Combin. Theory, Ser A 79 (1997), 1-35.
    24. Mutafchiev, L., The largest tree in certain models of random forests, Random Struct. Alg. 13(1998), 211-228.
    25. Mutafchiev, L., A limit theorem concerning the likely shape of the Ferrers diagram, Discrete Math. Appl. 9(1999), 79-100.
    26. Mutafchiev, L., Combinatorial Analysis and Probabilities, (a textbook in Bulgarian), Sofia University, Sofia, 1988.

27. Mutafchiev, L., Large trees in certain models of random forests, Random†††††††††† Stuctures Algorithms., 13(1998),211-228.

28. Mutafchiev, L., A limit theorem concerning the likely shape of Ferrers Diagram, Discrete Math. Appl. 9(1999), 79-100.

29. Mutafchiev, L., Correction to "A limit theorem concerning the likely shape of Ferrers Diagram, Discrete Math. Appl. 9(1999), 79-100.", Discrete Math. Appl. 9(1999), 685-686

††††††††††† 30. Mutafchiev, L., Large distinct part sizes in a random integer partition,  ActaMath. Hung. 87(2000), 47-69. 

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