Asymptotics of permutations with nearly periodic patterns of rises and falls
The electronic journal of combinatorics, Tome 10 (2003)
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Ehrenborg obtained asymptotic results for nearly alternating permutations and conjectured an asymptotic formula for the number of permutations that have a nearly periodic run pattern. We prove a generalization of this conjecture, rederive the fact that the asymptotic number of permutations with a periodic run pattern has the form $Cr^{-n}\,n!$, and show how to compute the various constants. A reformulation in terms of iid random variables leads to an eigenvalue problem for a Fredholm integral equation. Tools from functional analysis establish the necessary properties.
Edward A. Bender; William J. Helton; L. Bruce Richmond. Asymptotics of permutations with nearly periodic patterns of rises and falls. The electronic journal of combinatorics, Tome 10 (2003). doi: 10.37236/1733
@article{10_37236_1733,
author = {Edward A. Bender and William J. Helton and L. Bruce Richmond},
title = {Asymptotics of permutations with nearly periodic patterns of rises and falls},
journal = {The electronic journal of combinatorics},
year = {2003},
volume = {10},
doi = {10.37236/1733},
zbl = {1031.05015},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1733/}
}
TY - JOUR AU - Edward A. Bender AU - William J. Helton AU - L. Bruce Richmond TI - Asymptotics of permutations with nearly periodic patterns of rises and falls JO - The electronic journal of combinatorics PY - 2003 VL - 10 UR - http://geodesic.mathdoc.fr/articles/10.37236/1733/ DO - 10.37236/1733 ID - 10_37236_1733 ER -
%0 Journal Article %A Edward A. Bender %A William J. Helton %A L. Bruce Richmond %T Asymptotics of permutations with nearly periodic patterns of rises and falls %J The electronic journal of combinatorics %D 2003 %V 10 %U http://geodesic.mathdoc.fr/articles/10.37236/1733/ %R 10.37236/1733 %F 10_37236_1733
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