16 citations · 69 across the 23 of their papers we have counts for
5 papers · 1 filter
Combinatorial interpretations of Lucas analogues of binomial coefficients and Catalan numbers
Curtis Bennett, Juan Carrillo, John Machacek +1
The Lucas sequence is a sequence of polynomials in s, and t defined recursively by {0}=0, {1}=1, and {n}=s{n-1}+t{n-2} for n >= 2. On specialization of s and t one can recover the…
Partial words with a unique position starting a square
John Machacek
We consider partial words with a unique position starting a power. We show that over a letter alphabet, a partial word with a unique position starting a square can contain at m…
Strong factorization and the braid arrangement fan
John Machacek
We establish strong factorization for pairs of smooth fans which are refined by the braid arrangement fan. Our method uses a correspondence between cones and preposets.
Reddening Sequences for Banff Quivers and the Class
Eric Bucher, John Machacek
We show that a reddening sequence exists for any quiver which is Banff. Our proof is combinatorial and relies on the triangular extension construction for quivers. The other facts…
Upper cluster algebras and choice of ground ring
Eric Bucher, John Machacek, Michael Shapiro
We initiate a study of the dependence on the choice of ground ring on the question of whether a cluster algebra is equal to its upper cluster algebra. A condition for when there is…