We consider bicolored maps, i.e. graphs which are drawn on surfaces, and construct a bijection between (i) oriented maps with arbitary face structure, and (ii) (weighted) non-oriented maps with exactly one face. Above, each non-oriented map is counted with a multiplicity which is based on the concept of the orientability generating series and the measure of orientability of a map. This bijection has the remarkable property of preserving the underlying bicolored graph. Our bijection shows equivalence between two explicit formulas for the top-degree of Jack characters, i.e. (suitably normalized) coefficients in the expansion of Jack symmetric functions in the basis of power-sum symmetric functions.
@article{10_37236_6718,
author = {Agnieszka Czy\.zewska-Jankowska and Piotr \'Sniady},
title = {Bijection between oriented maps and weighted non-oriented maps},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {3},
doi = {10.37236/6718},
zbl = {1367.05047},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6718/}
}
TY - JOUR
AU - Agnieszka Czyżewska-Jankowska
AU - Piotr Śniady
TI - Bijection between oriented maps and weighted non-oriented maps
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/6718/
DO - 10.37236/6718
ID - 10_37236_6718
ER -
%0 Journal Article
%A Agnieszka Czyżewska-Jankowska
%A Piotr Śniady
%T Bijection between oriented maps and weighted non-oriented maps
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/6718/
%R 10.37236/6718
%F 10_37236_6718
Agnieszka Czyżewska-Jankowska; Piotr Śniady. Bijection between oriented maps and weighted non-oriented maps. The electronic journal of combinatorics, Tome 24 (2017) no. 3. doi: 10.37236/6718
