@article{oai:ompu.repo.nii.ac.jp:00000517,
 author = {永田, 誠 and 武井, 由智 and NAGATA, Makoto and TAKEI, Yoshinori},
 journal = {大阪医科薬科大学 薬学部雑誌, Bulletin of the Faculty of Pharmacy, Osaka Medical and Pharmaceutical University},
 month = {Mar},
 note = {We consider a 2-dimensional version of Sur´anyi’s bijections for S´os permutations. Sur´anyi’s bijection
is a bijective map between the set of the short intervals appearing as the division of the unit interval
by the Farey sequence and the set of S´os permutations. A concept equivalent to Sur´anyi’s bijection
is a bijective map between the set of the short intervals by the Farey sequence and the set of the
inverses of S´os permutations. In this article, we attempt to give a 2-dimensional analogue of the latter
map. First, we introduce our 2D version, which we refer to as a ranking table, of the inverse of a S´os
permutation. Then we define small polygons, which are bounded by the lines of so-called Farey diagram
and some additional lines, as our 2D version of the short intervals by the Farey sequence. Based on
these definitions, we show that our map between the set of the small polygons and the set of the ranking
tables is a well-defined surjection. Also, an examination using a computer shows that the map is in fact
bijective, for all 81 cases (which can be reduced to 45 cases by a symmetry) which are chosen as the cases
in which the size of the ranking table is small. Furthermore, we show that our map is indeed injective
when the image of the map is restricted to the set of the ranking tables formed by the standard Young
tableaux. This restricted map may be interpreted as yet another Sur´anyi’s bijection which is different
from our 2D version. In fact, the domain which is similar to the short intervals by Farey sequences
appears for our bijective map into the set of Young tableaux. We also mention the triangles-quadrangles
conjecture for the Farey diagram in our context.},
 pages = {21--55},
 title = {S´os 置換に関するSur´anyiの全単射のある2次元版について},
 volume = {2},
 year = {2023},
 yomi = {ナガタ, マコト and タケイ, ヨシノリ}
}