Geodesic
Updown numbers and the initial monomials of the slope variety
The electronic journal of combinatorics, Tome 16 (2009) no. 1
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

Let $I_n$ be the ideal of all algebraic relations on the slopes of the ${n\choose2}$ lines formed by placing $n$ points in a plane and connecting each pair of points with a line. Under each of two natural term orders, the ideal of $I_n$ is generated by monomials corresponding to permutations satisfying a certain pattern-avoidance condition. We show bijectively that these permutations are enumerated by the updown (or Euler) numbers, thereby obtaining a formula for the number of generators of the initial ideal of $I_n$ in each degree.
DOI : 10.37236/171
Classification : 05A15, 05A05, 14N20
Mots-clés : permutations, pattern avoidance condition, enumeration, updown numbers, Euler numbers, number of generators, ideal 
@article{10_37236_171,
     author = {Jeremy L. Martin and Jennifer D. Wagner},
     title = {Updown numbers and the initial monomials of the slope variety},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/171},
     zbl = {1186.05014},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/171/}
}
TY  - JOUR
AU  - Jeremy L. Martin
AU  - Jennifer D. Wagner
TI  - Updown numbers and the initial monomials of the slope variety
JO  - The electronic journal of combinatorics
PY  - 2009
VL  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.37236/171/
DO  - 10.37236/171
ID  - 10_37236_171
ER  - 
%0 Journal Article
%A Jeremy L. Martin
%A Jennifer D. Wagner
%T Updown numbers and the initial monomials of the slope variety
%J The electronic journal of combinatorics
%D 2009
%V 16
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/171/
%R 10.37236/171
%F 10_37236_171
Jeremy L. Martin; Jennifer D. Wagner. Updown numbers and the initial monomials of the slope variety. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/171

Cité par Sources :