2 citations · 2 across the 5 of their papers we have counts for
6 papers · 1 filter
An analogue of distributivity for ungraded lattices
Hugh Thomas
In this paper, we define a property, trimness, for lattices. Trimness is a not-necessarily-graded generalization of distributivity; in particular, if a lattice is trim and graded,…
Peg Jumping for Fun and Profit
David M. Bradley, Hugh Thomas
We consider the problem of determining the minimum number of moves needed to solve a certain one-dimensional peg puzzle. Let N be a positive integer. The puzzle apparatus consists…
Graded left modular lattices are supersolvable
Hugh Thomas
We provide a direct proof that a finite graded lattice with a maximal chain of left modular elements is supersolvable. This result was first established via a detour through EL-lab…
Tamari lattices and noncrossing partitions in type B and beyond
Hugh Thomas
The usual, or type A_n, Tamari lattice is a partial order on T_n^A, the triangulations of an (n+3)-gon. We define a partial order on T_n^B, the set of centrally symmetric triangula…
The number of terms in the permanent and the determinant of a generic circulant matrix
Hugh Thomas
Let A=(a_(ij)) be the generic n by n circulant matrix given by a_(ij)=x_(i+j), with subscripts on x interpreted mod n. Define d(n) (resp. p(n)) to be the number of terms in the det…
Maps between higher Bruhat orders and higher Stasheff-Tamari posets
Hugh Thomas
We make explict a description in terms of convex geometry of the higher Bruhat orders B(n,d) sketched by Kapranov and Voevodsky. We give an analogous description of the higher Stas…