Arrow-type semigroupoids / transitive relation digraphs refined by arrow count, complete to 10 objects
Attila Egri-Nagy, Chrystopher L. Nehaniv · arXiv (Cornell University) · 2025
Complete enumeration of arrow-type semigroupoids by objects and arrows for 1 to 10 objects,equivalently transitive relation digraphs on n unlabelled points with no isolated point, counted bynumber of related pairs. Computed from the Brinkmann-McKay structure theorem as a weighted Burnside count over unlabelledposets, rather than by searching semigroupoids. Extends Table 1 of arXiv:2509.00837 (Egri-Nagy andNehaniv, 2025), which gives the refinement completely to 7 objects and partially at 8; columns 8, 9and 10 are complete here. Contents: two independent implementations (one level-storing, one streaming posets by McKaycanonical augmentation with automorphism groups collapsed to cycle partitions), the full table asCSV, the OEIS b-file, a benchmark, and the run logs. Verification: unlabelled poset counts match A000112 for m = 8 is what this work adds. Code is MIT licensed; the data and results are released CC0.