1Departamento de Matemáticas Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional 2Departamento de Sistemas Universidad Autónoma Metropolitana Azcapotzalco
The electronic journal of combinatorics, Tome 24 (2017) no. 4
An intercalate matrix $M$ of type $[r,s,n]$ is an $r\times s$ matrix with entries in $\{1,2,\dotsc,n\}$ such that all entries in each row are distinct, all entries in each column are distinct, and all $2 \times 2$ submatrices of $M$ have either $2$ or $4$ distinct entries. Yuzvinsky's Conjecture on intercalate matrices claims that the smallest $n$ for which there is an intercalate matrix of type $[r,s,n]$ is the Hopf-Stiefel function $r \circ s$. In this paper we prove that Yuzvinsky's Conjecture is asimptotically true for $\frac{5}{6}$ of integer pairs $(r,s)$. We prove the Conjecture for $r\le 8$, and we study it in the range $r,s\le 32$.
Isidoro Gitler
1
;
Enrique Reyes
1
;
Francisco Javier Zaragoza Martínez
2
1
Departamento de Matemáticas
Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional
2
Departamento de Sistemas
Universidad Autónoma Metropolitana Azcapotzalco
@article{10_37236_6322,
author = {Isidoro Gitler and Enrique Reyes and Francisco Javier Zaragoza Mart{\'\i}nez},
title = {A step towards {Yuzvinsky's} conjecture},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {4},
doi = {10.37236/6322},
zbl = {1373.05032},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6322/}
}
TY - JOUR
AU - Isidoro Gitler
AU - Enrique Reyes
AU - Francisco Javier Zaragoza Martínez
TI - A step towards Yuzvinsky's conjecture
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/6322/
DO - 10.37236/6322
ID - 10_37236_6322
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%A Francisco Javier Zaragoza Martínez
%T A step towards Yuzvinsky's conjecture
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/6322/
%R 10.37236/6322
%F 10_37236_6322
Isidoro Gitler; Enrique Reyes; Francisco Javier Zaragoza Martínez. A step towards Yuzvinsky's conjecture. The electronic journal of combinatorics, Tome 24 (2017) no. 4. doi: 10.37236/6322
