The relation between the refined face numbers of the permutohedra and the formal series expansion of the reciprocal of a function (exponential generating function, formal Taylor series) is given in the OEIS entries A049019 and A133314 and is reiterated in this MO-Q. What are some early references for this relation?
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asked Apr 30, 2016 at 21:51
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1$\begingroup$ Could you reproduce the statement please? $\endgroup$– მამუკა ჯიბლაძეCommented May 6, 2016 at 5:58
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$\begingroup$ Sorry not for me. Maybe you could state something in the question? The OEIS links both start labyrinths of links where I became lost very soon. The last one does not contain any mention of permutohedra itself. The first one does, but I could not extract a clean statement from there. For example, what does "refined face polynomial" mean? $\endgroup$– მამუკა ჯიბლაძეCommented May 6, 2016 at 8:37
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$\begingroup$ What I am familiar with is the associahedral case. Do you mean that associahedra are to ogf as permutohedra to egf? $\endgroup$– მამუკა ჯიბლაძეCommented May 6, 2016 at 8:43
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1$\begingroup$ Thanks, this comment was indeed helpful. I now understand. Still I believe you make it hard for a first reader. Following the link one sees "This array is related to the reciprocal of an e.g.f. as sketched in A133314." and then an illustration, which makes it clear in principle, but still does not provide any rigorous statement. What is still not clear to me for example, is whether it is a proven fact or a conjectural relationship? $\endgroup$– მამუკა ჯიბლაძეCommented May 6, 2016 at 9:01
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2$\begingroup$ You should certainly reproduce the statement in the body of the question. $\endgroup$– Neil StricklandCommented May 6, 2016 at 9:27
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