S A Joni and G-C Rota. Coalgebras and bialgebras in combinatorics. Studies in Applied Mathematics, 61:93-139, 1979. Home/Search Document Not in Database Summary Related Articles Check |
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The Shuffle Hopf Algebra and Noncommutative Full Completeness - Blute, Scott (1996) (5 citations) (Correct)
.... rule to the fully noncommutative logic of [3] The corresponding version of proof net is also described in [38] This theory has subsequently been used substantially by Retor e in his work on linguistics [31] The Hopf algebra which provides our semantics is an example of the incidence algebras of [22, 33]. It is also refered to as a shuffle algebra in [10] which is the name we have chosen to use. Given a sequent in linear logic, we assign a vector space of dinaturals which are uniform with respect to this Hopf algebra, and show that it is generated by the denotations of (equivalence classes of) ....
....and concurrent computation, an important notion is that of interleaving or merging of input streams of data. Benson [10] observed that this process has a natural algebraic structure, which led him to consider the shuffle algebra. Such structures also arise in a fundamental way in combinatorics [22, 33], as such Hopf algebras provide an algebraic framework for the study of generating functions. Connections to combinatorics are further established via Joyal s notion of 2 species [23] a functorial framework for analyzing generating functions. Species were then generalized and given a ....
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S. Joni, G.C. Rota, Coalgebras and Bialgebras in Combinatorics, Studies in Applied Mathematics 61, p. 93-139, (1979).
Universal Constructions in Umbral Calculus - Ray (1996) (1 citation) (Correct)
....study of umbral calculus lies in the category CR of coassociative coalgebras over R, together with the category AR of dual algebras. Additional features such as gradings and Hopf algebra structures may naturally be present in certain circumstances. This viewpoint was conceived by Joni and Rota [5] and developed by Nichols and Sweedler [8] although both works continued to suggest that R should usually be a field. Our purpose here is to popularize elements of umbral calculus which have already been translated into the language of universal algebra, and to introduce new and related ....
S A Joni and G-C Rota, Coalgebras and bialgebras in combinatorics, Studies in Applied Mathematics 61 (1979), 93--139
Combinatorial Models For Coalgebraic Structures - Ray, Schmitt (1997) (Correct)
....the notion of CW complex, and is also geared to future applications in algebraic topology and the theory of formal group laws. 1. Introduction The theory of coalgebras and Hopf algebras was first developed by algebraic topologists more than fifty years ago. Since the seminal work of Joni and Rota [13], applications to combinatorial mathematics have grown steadily in prominence, motivated by the principle that a diagonal, or coproduct map, is an efficient medium for encoding information about the different ways in which a discrete structure may be split into two pieces. This principle has often ....
.... i ; where B n;k denotes the partial Bell polynomial. The rational expression ffi ( k ) k 1) X i j=k (1 1 2 2 3 Delta Delta Delta ) i 1 j Omega i (i 1) 6.22) is equivalent. The Hopf algebra Z (F) was called the Fa a di Bruno Hopf algebra by Joni and Rota in [13], and was first studied by Doubilet in [3] the expression 24 NIGEL RAY AND WILLIAM SCHMITT (6.22) shows that it represents the group scheme of formal Hurwitz series under substitution. Its antipode satisfies ( k ) X i1 ( Gamma1) i B k i;i (0; 1 ; 2 ; for all k 1. A ....
S. A. Joni and G.-C. Rota. Coalgebras and bialgebras in combinatorics. Studies in Applied Mathematics, 61:93--139, 1979.
Colimits, Stanley-Reisner Algebras, and Loop Spaces - Panov, Ray, Vogt (Correct)
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S A Joni and G-C Rota. Coalgebras and bialgebras in combinatorics. Studies in Applied Mathematics, 61:93-139, 1979.
Universal Constructions in Umbral Calculus - Nig El Ray (1996) (1 citation) (Correct)
No context found.
S A Joni and G-C Rota, Coalgebras and bialgebras in combinatorics, Studies in Applied Mathematics 61 (1979), 93--139
Sequences of Symmetric Functions of Binomial Type - Loeb (1994) (Correct)
No context found.
S. A. Joni, and G.-C. Rota, Coalgebras and Bialgebras in Combinatorics, Studies in Applied Mathematics, 61 (1979), 93--139.
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