Changes between Version 3 and Version 4 of Ticket #14542, comment 4


Ignore:
Timestamp:
07/30/13 09:14:36 (9 years ago)
Author:
darij
Comment:

Legend:

Unmodified
Added
Removed
Modified
  • Ticket #14542, comment 4

    v3 v4  
    1919On 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
    2020
    21 p_\lambda \boxdot p_\mu = \prod_{i,j} p_{\lcm(\lambda_i, \lambda_j)}^{\gcd(\lambda_i, \lambda_j)}
     21p_\lambda \boxdot p_\mu = \prod_{i,j} p_{\lcm(\lambda_i, \mu_j)}^{\gcd(\lambda_i, \mu_j)}
    2222
    2323for 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?