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2014 | 12 | 9 | 1372-1381
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On colored set partitions of type B n

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Generalizing Reiner’s notion of set partitions of type B n, we define colored B n-partitions by coloring the elements in and not in the zero-block respectively. Considering the generating function of colored B n-partitions, we get the exact formulas for the expectation and variance of the number of non-zero-blocks in a random colored B n-partition. We find an asymptotic expression of the total number of colored B n-partitions up to an error of O(n −1/2log7/2 n], and prove that the centralized and normalized number of non-zero-blocks is asymptotic normal over colored B n-partitions.
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  • [1] Bender E.A., Central and local limit theorems applied to asymptotic enumeration, J. Combin. Theory Ser. A, 1973, 15, 91–111
  • [2] Benoumhani M., On Whitney numbers of Dowling lattices, Discrete Math., 1996, 159(1–3), 13–33
  • [3] Björner A., Brenti F., Combinatorics of Coxeter Groups, Grad. Texts in Math., 231, Springer, New York, 2005
  • [4] Björner A., Sagan B.E., Subspace arrangements of type B n and D n, J. Algebraic Combin., 1996, 5(4), 291–314
  • [5] de Bruijn N.G., Asymptotic Methods in Analysis, 3rd ed., Dover, New York, 1981
  • [6] Chen W.Y.C., Wang D.G.L., The limiting distribution of the q-derangement numbers, European J. Combin., 2010, 31(8), 2006–2013
  • [7] Corless R.M., Gonnet G.H., Hare D.E.G., Jeffrey D.J., Knuth D.E., On the Lambert W function, Adv. Comput. Math., 1996, 5(4), 329–359
  • [8] Dowling T.A., A class of geometric lattices based on finite groups, J. Combin. Theory Ser. B, 1973, 14, 61–86
  • [9] Drmota M., Gittenberger B., Klausner T., Extended admissible functions and Gaussian limiting distributions, Math. Comp., 2005, 74(252), 1953–1966
  • [10] Flajolet P., Sedgewick R., Analytic Combinatorics, Cambridge University Press, Cambridge, 2009
  • [11] Gittenberger B., Mandlburger J., Hayman admissible functions in several variables, Electron. J. Combin., 2006, 13(1), #106
  • [12] Goresky M., MacPherson R., Stratified Morse Theory, Ergeb. Math. Grenzgeb., 14, Springer, Berlin, 1988
  • [13] Harper L.H., Stirling behavior is asymptotically normal, Ann. Math. Statist., 1967, 38, 410–414
  • [14] Harris B., Schoenfeld L., Asymptotic expansions for the coefficients of analytic functions, Illinois J. Math., 1968, 12, 264–277
  • [15] Hayman W.K., A generalisation of Stirling’s formula, J. Reine Angew. Math., 1956, 196, 67–95
  • [16] Humphreys J.E., Reflection Groups and Coxeter Groups, Cambridge Stud. Adv. Math., 29, Cambridge University Press, Cambridge, 1990
  • [17] Karlin S., Total Positivity, I, Stanford University Press, Stanford, 1968
  • [18] Liu L.L., Wang Y., A unified approach to polynomial sequences with only real zeros, Adv. in Appl. Math., 2007, 38(4), 542–560
  • [19] Mansour T., Combinatorics of Set Partitions, Discrete Math. Appl. (Boca Raton), CRC Press, Boca Raton, 2013
  • [20] Odlyzko A.M., Asymptotic enumeration methods, In: Handbook of Combinatorics, 2, Elsevier, Amsterdam, 1995, 1063–1229
  • [21] Pitman J., Probabilistic bounds on the coefficients of polynomials with only real zeros, J. Combin. Theory Ser. A, 1997, 77(2), 279–303
  • [22] Reiner V., Non-crossing partitions for classical reflection groups, Discrete Math., 1997, 177(1–3), 195–222
  • [23] Sachkov V.N., Probabilistic Methods in Combinatorial Analysis, Encyclopedia Math. Appl., 56, Cambridge University Press, Cambridge, 1997
  • [24] Salvy B., Shackell J., Symbolic asymptotics: multiseries of inverse functions, J. Symbolic Comput., 1999, 27(6), 543–563
  • [25] Schoenberg I.J., On the zeros of the generating functions of multiply positive sequences and functions, Ann. of Math., 1955, 62(3), 447–471
  • [26] Schrödinger E., Statistical Thermodynamics, 2nd ed., Dublin Institute for Advanced Studies, Cambridge University Press, New York, 1962
  • [27] Stanley R.P., Enumerative Combinatorics, I, 2nd ed., Cambridge Stud. Adv. Math., 49, Cambridge University Press, Cambridge, 1997
  • [28] White J.A., On the Complement of r-disjoint k-parabolic Subspace Arrangements, PhD thesis, Arizona State University, 2010
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