The complexes of Peter Sellers (Q1915395)

\textit{P. Sellers} [SIAM J. Appl. Math. 15, 13-68 (1967; Zbl 0175.20004)] defines partition complexes \(C^\lambda\) corresponding to partitions \(\lambda\) of a positive integer \(n\). The paper puts Sellers' construction into a more general context. Let \(K\) be a field (of characteristic zero) and \(K[X]\) the polynomial algebra in a finite set of indeterminates. For a multicomplex \(M\) of monomials of \(K[X]\), the author defines homology groups \(H^{\varepsilon, \eta} (M)\) and \(H^\omega (M)\) determined by a pair of \(K\)-algebra maps \(\varepsilon, \eta : K [X] \to K\) and a map \(\omega : X \to K\), respectively. Then an isomorphism \(\zeta : H^\omega (M) \to H^{\varepsilon, \eta} (M)\) is shown and Sellers' results are deduced as special cases.