Asymptotics of permutations with nearly periodic patterns of rises and falls
The electronic journal of combinatorics, Tome 10 (2003)
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.
@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
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
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