A chord diagram consists of a circle, called the backbone, with line segments, called chords, whose endpoints are attached to distinct points on the circle. The genus of a chord diagram is the genus of the orientable surface obtained by thickening the backbone to an annulus and attaching bands to the inner boundary circle at the ends of each chord. Variations of this construction are considered here, where bands are possibly attached to the outer boundary circle of the annulus. The genus range of a chord diagram is the genus values over all such variations of surfaces thus obtained from a given chord diagram. Genus ranges of chord diagrams for a fixed number of chords are studied. Integer intervals that can be, and those that cannot be, realized as genus ranges are investigated. Computer calculations are presented, and play a key role in discovering and proving the properties of genus ranges.

中文翻译：

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和弦图的属域

弦图由一个称为主干的圆和称为弦的线段组成，其端点连接到圆上的不同点。弦图的亏格是通过将骨架加厚为环面并将带附加到每个弦末端的内边界圆而获得的可定向表面的亏格。这里考虑了这种构造的变体，其中带可能附接到环面的外边界圆。弦图的亏格范围是从给定弦图获得的所有此类表面变化的亏格值。研究了固定数量和弦的和弦图的属域。研究了可以和不能实现为属范围的整数区间。提出了计算机计算，并在发现和证明属范围的特性方面发挥了关键作用。