A Rational-Function Identity Related to the Murnaghan–Nakayama Formula for the Characters of Sn


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Abstract

The Murnaghan–Nakayama formula for the characters of Sn is derived from Young's seminormal representation, by a direct combinatorial argument. The main idea is a rational function identity which when stated in a more general form involves Möbius functions of posets whose Hasse diagrams have a planar embedding. These ideas are also used to give an elementary exposition of the main properties of Young's seminormal representations.

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