Guilherme Zeus Dantas e Moura

Recent Publications (all)

• Probabilistic Entry Swapping Bijections for Non-Attacking Fillings (2025)

  arXiv

  Guilherme Zeus Dantas e Moura Olya Mandelshtam

  
  
  Abstract

  Non-attacking fillings are combinatorial objects central to the theory of Macdonald polynomials. A probabilistic bijection for partition-shaped non-attacking fillings was introduced by Mandelshtam (2024) to prove a compact formula for symmetric Macdonald polynomials. In this work, we generalize this probabilistic bijection to composition-shaped non-attacking fillings. As an application, we provide a bijective proof to extend a symmetry theorem for permuted-basement Macdonald polynomials established by Alexandersson (2019), proving a version with fewer assumptions.

• Cluster monomials in graph Laurent phenomenon algebras (2024)

  arXiv

  Ramanuja Charyulu Telekicherla Kandalam Guilherme Zeus Dantas e Moura Dora Woodruff

  
  To appear in Algebraic Combinatorics
  Abstract

  Laurent Phenomenon algebras, first introduced by Lam and Pylyavskyy, are a generalization of cluster algebras that still possess many salient features of cluster algebras. Graph Laurent Phenomenon algebras, defined by Lam and Pylyavskyy, are a subclass of Laurent Phenomenon algebras whose structure is given by the data of a directed graph. The main result of this paper is that the cluster monomials of a graph Laurent Phenomenon algebra form a linear basis, conjectured by Lam and Pylyavskyy and analogous to a result for cluster algebras by Caldero and Keller.