论文标题
晶格交叉的加泰罗尼亚州的系数II：$θ_{a} $的应用 - 状态扩展
Coefficients of Catalan States of Lattice Crossing II: Applications of $Θ_{A}$-state Expansions
论文作者
论文摘要
J.H.如本文所示，当$α$满足其他条件时，拔出多项式因子。我们使用此结果以及我们先前工作中引入的$θ_{a} $ - $ c（a）$ c（a）加泰罗尼亚州$ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ l（m，n）$。特别是，我们表明$ c（a）$因素当$ c $具有具有一些特殊属性的弧线时。在许多情况下，这为计算$ c（a）$而产生了更有效的方法。作为一种应用程序，我们为加泰罗尼亚州$ L（M，3）$的加泰罗尼亚州的系数提供了封闭式公式。
Plucking polynomial of a plane rooted tree with a delay function $α$ was introduced in 2014 by J.H.~Przytycki. As shown in this paper, plucking polynomial factors when $α$ satisfies additional conditions. We use this result and $Θ_{A}$-state expansion introduced in our previous work to derive new properties of coefficients $C(A)$ of Catalan states $C$ resulting from an $m \times n$-lattice crossing $L(m,n)$. In particular, we show that $C(A)$ factors when $C$ has arcs with some special properties. In many instances, this yields a more efficient way for computing $C(A)$. As an application, we give closed-form formulas for coefficients of Catalan states of $L(m,3)$.
