Zobrazeno 1 - 10
of 94
pro vyhledávání: '"Machacek, John"'
Autor:
Machacek, John
We introduce totally nonnegative Grassmannians over finite fields where an element of a finite field is nonnegative if it is a square of an element of the finite field. Explicit point counts are given in some special cases where we find new interpret
Externí odkaz:
http://arxiv.org/abs/2410.06177
Autor:
Hersh, Patricia, Machacek, John
This paper proves that the facet-ridge incidence graph of the order complex of any finite geometric lattice of rank $r$ has diameter at most ${r \choose 2}$. A key ingredient is the well-known fact that every ordering of the atoms of any finite geome
Externí odkaz:
http://arxiv.org/abs/2408.09197
Autor:
Machacek, John, Nasr, George D.
In this paper, we study positroids and its overlap with two classes of matroids: transversal and paving matroids. We exhibit a new class of fundamental transversal matroids and classify the Le-diagram for rank two transversal positroids. We also esta
Externí odkaz:
http://arxiv.org/abs/2401.02053
Autor:
Machacek, John
Breuer and Klivans defined a diverse class of scheduling problems in terms of Boolean formulas with atomic clauses that are inequalities. We consider what we call graph-like scheduling problems. These are Boolean formulas that are conjunctions of dis
Externí odkaz:
http://arxiv.org/abs/2308.11587
Autor:
Machacek, John, Ovenhouse, Nicholas
We consider $q$-binomial coefficients built from the $q$-rational and $q$-real numbers defined by Morier-Genoud and Ovsienko in terms of continued fractions. We establish versions of both the $q$-Pascal identity and the $q$-binomial theorem in this s
Externí odkaz:
http://arxiv.org/abs/2301.08185
Autor:
Bucher, Eric, Machacek, John
Publikováno v:
Arnold Mathematical Journal (2023)
In this article, we will expand on the notions of maximal green and reddening sequences for quivers associated to cluster algebras. The existence of these sequences has been studied for a variety of applications related to Fomin and Zelevinsky's clus
Externí odkaz:
http://arxiv.org/abs/2204.03212
Autor:
Machacek, John
Walnut is a software that using automata can prove theorems in combinatorics on words about automatic sequences. We are able to apply this software to both prove new results as well as reprove some old results on avoiding squares and cubes in partial
Externí odkaz:
http://arxiv.org/abs/2201.05954
Autor:
Hallam, Joshua, Machacek, John
To any poset $P$, we associate a convex cone called a braid cone. We also associate a fan and study the toric varieties the cone and fan define. The fan always defines a smooth toric variety $X_P$, while the toric variety $U_P$ of the cone may be sin
Externí odkaz:
http://arxiv.org/abs/2112.15308
Autor:
Machacek, John, Ovenhouse, Nicholas
We introduce a family of discrete dynamical systems which includes, and generalizes, the mutation dynamics of rank two cluster algebras. These systems exhibit behavior associated with integrability, namely preservation of a symplectic form, and in th
Externí odkaz:
http://arxiv.org/abs/2109.06927
Autor:
Machacek, John
Publikováno v:
Enumer. Combin. Appl. 2:1 (2022) Article S2R3
We work with lattice walks in $\mathbb{Z}^{r+1}$ using step set $\{\pm 1\}^{r+1}$ that finish with $x_{r+1} = 0$. We further impose conditions of avoiding backtracking (i.e. $[v,-v]$) and avoiding consecutive steps (i.e. $[v,v]$) each possibly combin
Externí odkaz:
http://arxiv.org/abs/2105.02417