Monotone triangles and 312 pattern avoidance
The electronic journal of combinatorics, The Zeilberger Festschrift volume, Tome 18 (2011) no. 2
We demonstrate a natural bijection between a subclass of alternating sign matrices (ASMs) defined by a condition on the corresponding monotone triangle which we call the gapless condition and a subclass of totally symmetric self-complementary plane partitions defined by a similar condition on the corresponding fundamental domains or Magog triangles. We prove that, when restricted to permutations, this class of ASMs reduces to 312-avoiding permutations. This leads us to generalize pattern avoidance on permutations to a family of words associated to ASMs, which we call Gog words. We translate the gapless condition on monotone triangles into a pattern avoidance-like condition on Gog words associated. We estimate the number of gapless monotone triangles using a bijection with $p$-branchings.
DOI :
10.37236/2022
Classification :
05A05, 05A15, 05A19
Mots-clés : monotone triangle, pattern avoidance, bijection, permutation, alternating sign matrices, ASM, Magog triangles, words
Mots-clés : monotone triangle, pattern avoidance, bijection, permutation, alternating sign matrices, ASM, Magog triangles, words
@article{10_37236_2022,
author = {Arvind Ayyer and Robert Cori and Dominique Gouyou-Beauchamps},
title = {Monotone triangles and 312 pattern avoidance},
journal = {The electronic journal of combinatorics},
year = {2011},
volume = {18},
number = {2},
doi = {10.37236/2022},
zbl = {1243.05004},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2022/}
}
Arvind Ayyer; Robert Cori; Dominique Gouyou-Beauchamps. Monotone triangles and 312 pattern avoidance. The electronic journal of combinatorics, The Zeilberger Festschrift volume, Tome 18 (2011) no. 2. doi: 10.37236/2022
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