Composition sum identities related to the distribution of coordinate values in a discrete simplex

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dc.creatorMilson, Robert
dc.date2000-03-21
dc.date.accessioned2026-07-07T04:34:23Z
dc.date.available2026-07-07T04:34:23Z
dc.descriptionUtilizing spectral residues of parameterized, recursively defined sequences, we develop a general method for generating identities of composition sums. Specific results are obtained by focusing on coefficient sequences of solutions of first and second order, ordinary, linear differential equations. Regarding the first class, the corresponding identities amount to a proof of the exponential formula of labelled counting. The identities in the second class can be used to establish certain geometric properties of the simplex of bounded, ordered, integer tuples. We present three theorems that support the conclusion that the inner dimensions of such an order simplex are, in a certain sense, more ample than the outer dimensions. As well, we give an algebraic proof of a bijection between two families of subsets in the order simplex, and inquire as to the possibility of establishing this bijection by combinatorial, rather than by algebraic methods.
dc.descriptionAMSLatex, 16 pages
dc.identifierhttps://arxiv.org/abs/math/0003126
dc.identifierhttp://arxiv.org/abs/math/0003126
dc.identifierElectronic J. Combinatorics, 7 (2000), #R20
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58879
dc.subjectCombinatorics
dc.subject05A19, 05A20
dc.titleComposition sum identities related to the distribution of coordinate values in a discrete simplex
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