Acerbi (CNRS) has shown that a similar explanation can be provided for the other number: it is very close to the average of the tenth and eleventh Schröder–Hipparchus numbers, 310954, and counts bracketings of ten terms together with a negative particle. The problem of counting parenthesizations was introduced to modern mathematics by . Plutarch's recounting of Hipparchus's two numbers records a disagreement between Hipparchus and the earlier Stoic philosopher Chrysippus, who had claimed that the number of compound propositions that can be made from 10 simple propositions exceeds a million. Contemporary philosopher has argued that Chrysippus's calculation was the correct one, based on her analysis of Stoic logic. Bobzien reconstructs the calculations of both Chrysippus and Hipparchus, and says that showing how Hipparchus got his mathematics correct but his Stoic logic wrong can cast new light on the Stoic notions of conjunctions and assertibles. References External links The Hipparchus Operad, The n-Category Café, April 1, 2013 Integer sequences Enumerative combinatorics