The box parameter for words and permutations
Open Mathematics (2014)
- Volume: 12, Issue: 1, page 167-174
- ISSN: 2391-5455
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topHelmut Prodinger. "The box parameter for words and permutations." Open Mathematics 12.1 (2014): 167-174. <http://eudml.org/doc/269575>.
@article{HelmutProdinger2014,
abstract = {The box parameter for words counts how often two letters w j and w k define a “box” such that all the letters w j+1; ..., w k−1 fall into that box. It is related to the visibility parameter and other parameters on words. Three models are considered: Words over a finite alphabet, permutations, and words with letters following a geometric distribution. A typical result is: The average box parameter for words over an M letter alphabet is asymptotically given by 2n − 2n H M/M, for fixed M and n → ∞.},
author = {Helmut Prodinger},
journal = {Open Mathematics},
keywords = {Words; Permutations; q-enumeration; words; permutations; -enumeration; box parameter; visibility parameter},
language = {eng},
number = {1},
pages = {167-174},
title = {The box parameter for words and permutations},
url = {http://eudml.org/doc/269575},
volume = {12},
year = {2014},
}
TY - JOUR
AU - Helmut Prodinger
TI - The box parameter for words and permutations
JO - Open Mathematics
PY - 2014
VL - 12
IS - 1
SP - 167
EP - 174
AB - The box parameter for words counts how often two letters w j and w k define a “box” such that all the letters w j+1; ..., w k−1 fall into that box. It is related to the visibility parameter and other parameters on words. Three models are considered: Words over a finite alphabet, permutations, and words with letters following a geometric distribution. A typical result is: The average box parameter for words over an M letter alphabet is asymptotically given by 2n − 2n H M/M, for fixed M and n → ∞.
LA - eng
KW - Words; Permutations; q-enumeration; words; permutations; -enumeration; box parameter; visibility parameter
UR - http://eudml.org/doc/269575
ER -
References
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- [3] Flajolet P., Salvy B., Euler sums and contour integral representations, Experiment. Math., 1998, 7(1), 15–35 http://dx.doi.org/10.1080/10586458.1998.10504356 Zbl0920.11061
- [4] Gutin G., Mansour T., Severini S., A characterization of horizontal visibility graphs and combinatorics on words, Phys. A, 2011, 390(12), 2421–2428 http://dx.doi.org/10.1016/j.physa.2011.02.031
- [5] Prodinger H., Combinatorics of geometrically distributed random variables: inversions and a parameter of Knuth, Ann. Comb., 2001, 5(2), 241–250 http://dx.doi.org/10.1007/s00026-001-8010-z Zbl0994.05012
- [6] Prodinger H., A q-analogue of the path length of binary search trees, In: Mathematical Analysis of Algorithms, Algorithmica, 2001, 31(3), 433–441 17 Zbl0989.68035
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