A Unifying Framework for the $$\nu $$-Tamari Lattice and Principal Order Ideals in Young’s Lattice

Bell, Matias von; D’León, Rafael S. González; Cetina, Francisco A. Mayorga; Yip, Martha

doi:10.1007/s00493-023-00022-x

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2024

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Cited by 3 publications

(2 citation statements)

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“…More generally, [9] showed that order polytopes of strongly planar posets are flow polytopes. Subsequent work [2,8,7,5,17] built upon this connection between order and flow polytopes, but there was no interpretation in terms of alternating sign matrices. In this paper, we reunite these topics.…”

Section: Introductionmentioning

confidence: 99%

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Partial Permutation and Alternating Sign Matrix Polytopes

Heuer¹,

Striker²

2022

SIAM J. Discrete Math.

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We investigate analogues of alternating sign matrices, called partial alternating sign matrices. We prove bijections between these matrices and several other combinatorial objects. We use an analogue of Wieland's gyration on fully-packed loops, which we relate to the study of toggles and order ideals. Finally, we show that rowmotion on order ideals of a certain poset and gyration on partial fully-packed loop configurations are in equivariant bijection.

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Section: Introductionmentioning

confidence: 99%

“…In this paper, we reunite these topics. In particular, we were inspired by the polytope perspective on the ν-Tamari lattice in [17] to define and study an analogue of the ASM-CRY polytope of [9] using the partial alternating sign matrix polytope of [4]. Furthermore, we show this polytope is both an order and flow polytope.…”

Section: Introductionmentioning

confidence: 99%