Alternating sign matrices are known to be equinumerous with descending plane partitions, totally symmetric self-complementary plane partitions and alternating sign triangles, but no bijective proof for any of these equivalences has been found so far. In this paper we provide the first bijective proof of the operator formula for monotone triangles, which has been the main tool for several non-combinatorial proofs of such equivalences. In this proof, signed sets and sijections (signed bijections) play a fundamental role.
@article{10_37236_9082,
author = {Ilse Fischer and Matja\v{z} Konvalinka},
title = {A bijective proof of the {ASM} theorem. {I:} {The} operator formula},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {3},
doi = {10.37236/9082},
zbl = {1446.05006},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9082/}
}
TY - JOUR
AU - Ilse Fischer
AU - Matjaž Konvalinka
TI - A bijective proof of the ASM theorem. I: The operator formula
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/9082/
DO - 10.37236/9082
ID - 10_37236_9082
ER -
%0 Journal Article
%A Ilse Fischer
%A Matjaž Konvalinka
%T A bijective proof of the ASM theorem. I: The operator formula
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/9082/
%R 10.37236/9082
%F 10_37236_9082
Ilse Fischer; Matjaž Konvalinka. A bijective proof of the ASM theorem. I: The operator formula. The electronic journal of combinatorics, Tome 27 (2020) no. 3. doi: 10.37236/9082
