7 papers · 1 filter
The Ehrhart series of magic squares of orders seven and eight
Dun Qiu, Guoce Xin, Zihao Zhang
Let count the nonnegative integer matrices whose row sums, column sums, main-diagonal sum, and antidiagonal sum are all . We determine the Ehrhar…
The Schur positivity of
Dun Qiu, Minhao Zhang
Bergeron, Garsia, Haiman and Tesler conjectured in 1999 that, for all partitions , the polynomial has nonnegat…
The nonsymmetric compositional Delta theorem
Dun Qiu, Minhao Zhang
Extending the symmetric framework of D'Adderio and Mellit, we establish a nonsymmetric generalization of the compositional Delta theorem. Building on Blasiak et al.'s theory of fla…
On shortening universal words for multi-dimensional permutations
Sergey Kitaev, Dun Qiu
A universal word (u-word) for -dimensional permutations of length is a 2-dimensional word with rows, any size window of which is order-isomorphic to exactly one pe…
Symmetric statistics on rational Dyck paths
Lilan Dai, Shishuo Fu, Dun Qiu
Rational Dyck paths are the rational generalization of classical Dyck paths. They play an important role in Catalan combinatorics, and have multiple applications in algebra and geo…
Stanley's conjecture on the Schur positivity of distributive lattices
Grace M. X. Li, Dun Qiu, Arthur L. B. Yang +1
In this paper we solve an open problem on distributive lattices, which was proposed by Stanley in 1998. This problem was motivated by a conjecture due to Griggs, which equivalently…