Applications of estimates of the probability that a random dimensional subspace is of minimal weight
Author:
V. V. Masol
Translated by:
Oleg Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 69 (2003).
Journal:
Theor. Probability and Math. Statist. 69 (2004), 129140
MSC (2000):
Primary 60C05
Published electronically:
February 9, 2005
Fulltext PDF Free Access
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Abstract: We find nontrivial estimates of the probability that a random dimensional subspace of an dimensional vector space over a finite field is of minimal weight. The conditions are in Theorem 1 and in Theorem 2. Some applications of the estimates for finding the asymptotic behavior of the above probability are given.
 1.
George
E. Andrews, The theory of partitions, AddisonWesley
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Mathematics and its Applications, Vol. 2. MR 0557013
(58 #27738)
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V.
V. Masol, Asymptotics of the distribution of some characteristics
of random spaces over a finite field, Teor. Ĭmovīr. Mat.
Stat. 67 (2002), 97–103 (Ukrainian, with Ukrainian
summary); English transl., Theory Probab. Math. Statist.
67 (2003), 107–114. MR 1956623
(2003k:60022)
 3.
V.
I. Masol, Asymptotics of the number of certain
𝑘dimensional subspaces over a finite field, Mat. Zametki
59 (1996), no. 5, 729–736, 799 (Russian, with
Russian summary); English transl., Math. Notes 59 (1996),
no. 56, 525–530. MR 1445454
(98c:15005), http://dx.doi.org/10.1007/BF02308820
 4.
V. V. Masol, Some applications of the explicit formula for the probability that a random dimensional subspace is of minimal weight, Visnyk Kyiv University, Ser. Mathematics, Mechanics 10 (2003), 113117. (Ukrainian)
 1.
 G. Andrews, The Theory of Partitions, AddisonWesley, New York, 1976. MR 0557013 (58:27738)
 2.
 V. V. Masol, The limit behavior of the distribution of certain characteristics of random spaces over a finite field, Teor. Imovir. ta Matem. Statist. 67 (2002), 97103; English transl. in Theory Probab. Math. Statist. 67 (2003), 107114. MR 1956623 (2003k:60022)
 3.
 V. I. Masol, Asymptotics of the number of certain dimensional subspaces over a finite field, Mat. Zametki 59 (1996), no. 5, 729736; English. transl. in Math. Notes 59 (1996), no. 56, 525530. MR 1445454 (98c:15005)
 4.
 V. V. Masol, Some applications of the explicit formula for the probability that a random dimensional subspace is of minimal weight, Visnyk Kyiv University, Ser. Mathematics, Mechanics 10 (2003), 113117. (Ukrainian)
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Additional Information
V. V. Masol
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
vicamasol@pochtamt.ru
DOI:
http://dx.doi.org/10.1090/S0094900005006204
PII:
S 00949000(05)006204
Received by editor(s):
March 14, 2003
Published electronically:
February 9, 2005
Article copyright:
© Copyright 2005
American Mathematical Society
