Monotone triangles and 312 Pattern Avoidance
Arvind Ayyer, Robert Cori, Dominique Gouyou-Beauchamps

TL;DR
This paper establishes a bijection between certain classes of alternating sign matrices and plane partitions, generalizes 312 pattern avoidance to Gog words, and estimates their enumeration via p-branchings.
Contribution
It introduces the gapless condition on monotone triangles, connects it to pattern avoidance in permutations, and extends pattern avoidance concepts to Gog words.
Findings
Bijection between gapless ASMs and symmetric plane partitions.
Reduction of gapless ASMs to 312-avoiding permutations.
Enumeration of gapless monotone triangles using p-branchings.
Abstract
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 trangles into a pattern avoidance-like condition on Gog words associated. We estimate the number of gapless monotone triangles using a bijection with p-branchings.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
