Quasi-symmetric functions as polynomial functions on Young diagrams. (English) Zbl 1316.05120
Summary: We determine the most general form of a smooth function on Young diagrams, that is, a polynomial in the interlacing or multirectangular coordinates whose value depends only on the shape of the diagram. We prove that the algebra of such functions is isomorphic to quasi-symmetric functions, and give a noncommutative analog of this result.
MSC:
| 05E05 | Symmetric functions and generalizations |
| 05E10 | Combinatorial aspects of representation theory |
Software:
OEISOnline Encyclopedia of Integer Sequences:
Fubini numbers: number of preferential arrangements of n labeled elements; or number of weak orders on n labeled elements; or number of ordered partitions of [n].Exponential convolution of A000670(n), with A000670(0)=0, with the sequence of all ones alternating in sign.
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