Changes between Version 3 and Version 4 of Ticket #14542, comment 4
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- 07/30/13 09:14:36 (9 years ago)
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Ticket #14542, comment 4
v3 v4 19 19 On another note rather unrelated to Sage: The species viewpoint on the arithmetic product shows that the arithmetic product on the ring of symmetric functions (the one given by 20 20 21 p_\lambda \boxdot p_\mu = \prod_{i,j} p_{\lcm(\lambda_i, \ lambda_j)}^{\gcd(\lambda_i, \lambda_j)}21 p_\lambda \boxdot p_\mu = \prod_{i,j} p_{\lcm(\lambda_i, \mu_j)}^{\gcd(\lambda_i, \mu_j)} 22 22 23 23 for all partitions \lambda and \mu) is defined over the integers, not just over the rationals (despite the p_\lambda not forming a Z-basis of Symm). Is there an algebraic proof of this? It looks like a nice application of species to proving a nontrivial algebraic result. Is there a species-theoretical proof of the integrality of \Delta_3 in http://mathoverflow.net/questions/120924/is-the-renormalized-third-comultiplication-on-mathbfsymm-integral as well?
