8 papers
Sign variation and descents
Nantel Bergeron, Aram Dermenjian, John Machacek
For any and , let be the poset of projective equivalence classes of -vectors of length with sign variation bounded by , ordered by…
New Invariants for Permutations, Orders and Graphs
Jean-christophe Aval, Nantel Bergeron, John Machacek
We study the symmetric function and polynomial combinatorial invariants of Hopf algebras of permutations, posets and graphs. We investigate their properties and the relations among…
Building maximal green sequences via component preserving mutations
Eric Bucher, John Machacek, Evan Runburg +2
We introduce a new method for producing both maximal green and reddening sequences of quivers. The method, called component preserving mutations, generalizes the notion of direct s…
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.