论文标题
锁适合钥匙：锁多项式的晶体分析
Locks fit into keys: a crystal analysis of lock polynomials
论文作者
论文摘要
锁多项式和锁定kohnert Tableaux分别是关键多项式和钥匙kohnert tableaux的天然类似物。在本文中，我们将锁锁多项式与备受研究的密钥多项式进行了比较，并表明相同组成的键多项式和锁定多项式的差异是单一阳性。我们还检查了键和锁定多项式对称或准对称的条件。我们使用Key Kohnert Tableaux和Lock Kohnert Tableaux实现这些目标。特别是，对于关键的差异锁定锁的差异，我们关注晶体算子在Kohnert Tableaux上的行为。可以在键Kohnert Tableaux的顶点集中实现A类型晶体，并且我们以明确的组合定义显示出类似的晶体状结构在锁定kohnert tableaux的顶点集中存在。最后，我们构建了一个从Lock Kohnert Tableaux到关键的Kohnert Tableaux的注射式，举重的地图，该图形交织在一起。
Lock polynomials and lock Kohnert tableaux are natural analogues to key polynomials and key Kohnert tableaux, respectively. In this paper, we compare lock polynomials to the much-studied key polynomials and show that the difference of a key polynomial and lock polynomial for the same composition is monomial positive. We also examine the conditions for which key and lock polynomials are symmetric or quasisymmetric. We accomplish these goals combinatorially using key Kohnert tableaux and lock Kohnert tableaux. In particular, for the difference of a key minus a lock, we focus on the behavior of crystal operators on Kohnert tableaux. The Type A Demazure crystal can be realized on the vertex set of key Kohnert tableaux, and we show with an explicit combinatorial definition that a similar crystal-like structure exists on the vertex set of lock Kohnert tableaux. Finally, we construct an injective, weight-preserving map from lock Kohnert tableaux to key Kohnert tableaux that intertwines the crystal operators.
