The Voter Basis and the Admissibility of Tree Characters

Beveridge, Andrew; Calaway, Ian

doi:10.1007/s11083-021-09553-8

Cited by 1 publication

(4 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where omitting the doubletons gives the Ferrers diagram for the integer partition (4, 3, 2). Specifying the comparisons with singleton {5} is equivalent to placing a dot in each row of (4,3,2). Looking only at the top row, placing a 5 in the first box • means that 5 ≺ 41.…”

Section: ←→mentioning

confidence: 99%

“…Our final step is to count the boxes to the right of these dots, starting from the bottom row and moving up. This results in the lists (1, 2, 3), (0, 2, 3), (0, 1, 3) and (0, 0, 3) from L( [3]).…”

Section: ←→mentioning

confidence: 99%

“…Next, we consider extensions in Φ(I 7 ). Specifying the comparisons of singleton {7} with the doubletons in I 7 is equivalent to placing a dot in each row of the integer partition (6,5,4,3,2). Suppose that we place a 7 in the third box of the first row, corresponding to 62 ≺ 7 ≺ 63.…”

Section: ←→mentioning

confidence: 99%

“…In fact, they proved the stronger condition that linear extensions with at least one pair X, Y of proper nontrivial subsets satisfying condition (F2) are vanishingly rare. Other research on separable preferences focuses on the admissibility problem: which collection of subsets can occur as the collection of separable sets S, meaning that (F2) holds for any subsets X, Y ⊂ S and any Z ⊂ S, see [19,18,3].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

de Finetti Lattices and Magog Triangles

Beveridge¹,

Calaway²,

Heysse³

2019

Preprint

Self Cite

View full text Add to dashboard Cite

Let B n,2 denote the order ideal of the boolean lattice B n consisting of all subsets of size at most 2. Let F n,2 denote the poset extension of B n,2 induced by the rule: i < j implies {i} ≺ {j} and {i, k} ≺ {j, k}. We give an elementary bijection from the set F n,2 of linear extensions of F n,2 to the set of shifted standard Young tableau of shape (n, n − 1, . . . , 1), which are counted by the strict-sense ballot numbers. We find a more surprising result when considering the set F(1) n,2 of poset extensions so that each singleton is comparable with all of the doubletons. We show that F(1) n,2 is in bijection with magog triangles, and therefore is equinumerous with alternating sign matrices. We adopt our proof techniques to show that row reversal of an alternating sign matrix corresponds to a natural involution on gog triangles.

show abstract

Section: ←→mentioning

confidence: 99%

Section: ←→mentioning

confidence: 99%