Geodesic
Counting Multiderangements by Excedances
Séminaire lotharingien de combinatoire, Tome 59 (2008-2010)

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We consider in this work the enumeration of multiderangements of a multiset n={1n1,2n2,...,mnm} by the number of excedances. We prove several properties, including the invariance under permutations of {n1,n2,...,nm}, the symmetry, the recurrence relation, the real-rootedness, and a combinatorial expansion, of the generating function dn(x) of multiderangements by excedances, thus generalizing the corresponding results for the classical derangements. By a further extension, the generating function for multipermutations by numbers of excedances and fixed points is also given. 

@article{SLC_2008-2010_59_a2,
     author = {Chak-On Chow},
     title = {Counting {Multiderangements} by {Excedances}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {59},
     year = {2008-2010},
     url = {http://geodesic.mathdoc.fr/item/SLC_2008-2010_59_a2/}
}
TY  - JOUR
AU  - Chak-On Chow
TI  - Counting Multiderangements by Excedances
JO  - Séminaire lotharingien de combinatoire
PY  - 2008-2010
VL  - 59
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2008-2010_59_a2/
ID  - SLC_2008-2010_59_a2
ER  - 
%0 Journal Article
%A Chak-On Chow
%T Counting Multiderangements by Excedances
%J Séminaire lotharingien de combinatoire
%D 2008-2010
%V 59
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2008-2010_59_a2/
%F SLC_2008-2010_59_a2
Chak-On Chow. Counting Multiderangements by Excedances. Séminaire lotharingien de combinatoire, Tome 59 (2008-2010). http://geodesic.mathdoc.fr/item/SLC_2008-2010_59_a2/