Differential posets
Copyright policy )Differential posets
The author has introduced a class of partially ordered sets, called differential posets, with many remarkable combinatorial and algebraic properties. The problem is concerned with counting of saturated chains, \(x_ 1\mu^{n- 1}>...>\mu^ 0=\phi,\) where \(\lambda^ i\) and \(\mu^ i\) are partitions of i, is equal to \(n!\). If P is a graded poset then \(\rho\) denotes its rank function, i.e., if \(x\in P\) then \(\rho(x)\) is the length \(\ell\) of the longest chain \(x_ 0
Young's lattice, Hasse walks, Combinatorial aspects of partitions of integers, Partial orders, general, Exact enumeration problems, generating functions, saturated chains, Representations of finite symmetric groups, differential posets, spectrum of the adjacency matrix
Young's lattice, Hasse walks, Combinatorial aspects of partitions of integers, Partial orders, general, Exact enumeration problems, generating functions, saturated chains, Representations of finite symmetric groups, differential posets, spectrum of the adjacency matrix
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