.
_:N035fcaa1bbbb45a7a98c944003358af1 "10.1007/s00006-007-0063-6" .
"en" .
.
.
.
_:N7a0ba1570d314a14b95094707919a060 "18" .
"G. Stacey" .
"Advances in Applied Clifford Algebras" .
_:N9ee34fc91d3d43eebf98a8e5564fdc03 .
.
"research_article" .
.
_:N011203dd4666486db7d3bf253c7f046f .
"75-92" .
_:N8d7bd5cf9fe24d3f8d5b080448b53896 .
.
.
"Pure Mathematics" .
"Mathematical Sciences" .
"Department of Mathematics and Statistics, Southern Illinois University Edwardsville, 62026-1653, Edwardsville, IL, USA" .
_:N9ee34fc91d3d43eebf98a8e5564fdc03 .
_:N7a0ba1570d314a14b95094707919a060 .
_:N4a15190366ce4ebfb4437643e62b8a81 "Springer Nature - SN SciGraph project" .
_:N8d7bd5cf9fe24d3f8d5b080448b53896 "pub.1006910548" .
"2008-02" .
_:Na856d18750c447d6a5e25d69f4e814b1 .
_:N8d7bd5cf9fe24d3f8d5b080448b53896 "dimensions_id" .
_:Na856d18750c447d6a5e25d69f4e814b1 .
"Norms and Generating Functions in Clifford Algebras" .
"2019-04-10T19:03" .
_:N4a15190366ce4ebfb4437643e62b8a81 .
.
.
_:N8d7bd5cf9fe24d3f8d5b080448b53896 .
.
.
_:N9ee34fc91d3d43eebf98a8e5564fdc03 "1" .
_:N011203dd4666486db7d3bf253c7f046f "readcube_id" .
_:Na856d18750c447d6a5e25d69f4e814b1 .
_:N035fcaa1bbbb45a7a98c944003358af1 "doi" .
_:N4a15190366ce4ebfb4437643e62b8a81 .
"articles" .
"Staples" .
"1661-4909" .
.
_:N011203dd4666486db7d3bf253c7f046f .
_:N011203dd4666486db7d3bf253c7f046f "20eb1e157db4c38fd9c160077c8754c879aa61a9f3390188157ded740a5d619c" .
"https://scigraph.springernature.com/explorer/license/" .
_:N035fcaa1bbbb45a7a98c944003358af1 .
"2008-02-01" .
.
"Generating functions are commonly used in combinatorics to recover sequences from power series expansions. Convergence of formal power series in Clifford algebras of arbitrary signature is discussed. Given , powers of u are recovered by expanding (1 \u2212 tu)\u22121 as a polynomial in t with Clifford-algebraic coefficients. It is clear that (1 \u2212 tu)(1 + tu + t2u2 + ...) = 1, provided the sum (1 + tu + t2u2 + ...) exists, in which case um is the Cliffordalgebraic coefficient of tm in the series expansion of (1 \u2212 tu)\u22121. In this paper, conditions on for the existence of (1 \u2212 tu)\u22121 are given, and an explicit formulation of the generating function is obtained. Allowing A to be an m \u00D7 m matrix with entries in , a \u201CClifford-Frobenius\u201D norm of A is defined. Norm inequalities are then considered, and conditions for the existence of (I \u2212 tA)\u22121 are determined. As an application, adjacency matrices for graphs are defined with vectors of as entries. For positive odd integer k > 3, k-cycles based at a fixed vertex of a graph are enumerated by considering the appropriate entry of Ak. Moreover, k-cycles in finite graphs are enumerated and expected numbers of k-cycles in random graphs are obtained from the norm of the degree-2k part of tr(1 \u2212 tu)\u22121. Unlike earlier work using commutative subalgebras of , this approach represents a \u201Ctrue\u201D application of Clifford algebras to graph theory." .
"Southern Illinois University Edwardsville" .
"0188-7009" .
_:N035fcaa1bbbb45a7a98c944003358af1 .
"false"^^ .
_:N7a0ba1570d314a14b95094707919a060 .
"http://link.springer.com/10.1007/s00006-007-0063-6" .
.
.