We introduce two classes of morphisms over the alphabet $A=\{0,1\}$ whose fixed points contain infinitely many antipalindromic factors. An antipalindrome is a finite word invariant under the action of the antimorphism $\mathrm{E}:{\{0,1\}}^{\ast }\to {\{0,1\}}^{\ast }$, defined by $\mathrm{E}(w_1\cdots w_n)=(1-w_n)\cdots (1-w_1)$. We conjecture that these two classes contain all morphisms (up to conjugation) which generate infinite words with infinitely many antipalindromes. This is an analogue to the famous HKS conjecture concerning infinite words containing infinitely many palindromes. We prove our conjecture for two special classes of morphisms, namely (i) uniform morphisms and (ii) morphisms with fixed points containing also infinitely many palindromes.

我们介绍字母表上的两类变态 $\mathrm{一种}=\{0，\mathrm{1个}\}$其固定点包含无限多个抗回文因子。反回文症是在反同构作用下的有限词不变式$\mathrm{Ë}：{\{0，\mathrm{1个}\}}^{\ast }\to {\{0，\mathrm{1个}\}}^{\ast }$， 被定义为 $\mathrm{Ë}（w_{\mathrm{1个}}\cdots w_{ñ}）=（\mathrm{1个}-w_{ñ}）\cdots （\mathrm{1个}-w_{\mathrm{1个}}）$。我们推测这两个类别包含所有词素（直至共轭），这些词素生成具有无限多个反回文词的无限词。这类似于著名的HKS猜想，该猜想涉及包含无限多个回文的无限单词。我们证明了我们对两种特殊的态射素的猜想，即（i）均匀态射素和（ii）固定点也包含无限多个回文的态射素。