无转角、无峰、无谷的Motzkin路径（规则与斜向）及其在条形图中的应用
Cornerless, peakless, valleyless Motzkin paths (regular and skew) and applications to bargraphs
AI总结：
本文研究无转角Motzkin路径（含斜向变体），通过生成函数和核方法计数UD与DU出现次数，并推广Deutsch-Elizalde双射以应用于条形图前缀分析。
摘要：
Motzkin路径由上升步、下降步和水平步组成，始终不低于$x$轴并最终回到$x$轴。本文也考虑了不要求回到$x$轴的情形。若路径中从不出现$UD$（或$DU$），则称该路径为无峰（或无谷）路径。若同时无峰且无谷，则称为无转角路径。Deutsch和Elizalde已通过双射将无转角Motzkin路径与条形图联系起来。因此，可以考虑用无转角Motzkin路径的前缀来代替条形图的前缀。本文将这一思想推广，通过计数$UD$和$DU$的出现次数来扩展研究。这些概念进一步推广到所谓的斜向Motzkin路径。方法上采用生成函数和核方法来计算显式形式。
英文摘要：
Motzkin paths consist of up-steps, down-steps, horizontal steps, never go below the $x$-axis and return to the $x$-axis. Versions where the return to the $x$-axis isn't required are also considered. A path is peakless (valleyless) if $UD$ (if $DU$) never occurs. If it is both peakless and valleyless, it is called cornerless. Deutsch and Elizalde have linked cornerless Motzkin paths and bargraphs bijectly. Thus, instead of prefixes of bargraphs one might consider prefixes of cornerless Motzkin paths. In this paper, this is extended by counting the occurrences of $UD$ resp., $DU$. The concepts are extended to so-called skew Motzkin paths. Methods are generating functions and the kernel method to compute explicit forms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
