The Subconstituent Algebra of an Association Scheme, (Part I)
Journal of Algebraic Combinatorics: An International Journal
Sperner theory
The Terwilliger algebra of the hypercube
European Journal of Combinatorics
New upper bounds for nonbinary codes based on the Terwilliger algebra and semidefinite programming
Journal of Combinatorial Theory Series A - Special issue in honor of Jacobus H. van Lint
Enumerative Combinatorics: Volume 1
Enumerative Combinatorics: Volume 1
New code upper bounds from the Terwilliger algebra and semidefinite programming
IEEE Transactions on Information Theory
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The de Bruijn---Tengbergen---Kruyswijk (BTK) construction is a simple algorithm that produces an explicit symmetric chain decomposition of a product of chains. We linearize the BTK algorithm and show that it produces an explicit symmetric Jordan basis (SJB). In the special case of a Boolean algebra, the resulting SJB is orthogonal with respect to the standard inner product and, moreover, we can write down an explicit formula for the ratio of the lengths of the successive vectors in these chains (i.e., the singular values). This yields a new constructive proof of the explicit block diagonalization of the Terwilliger algebra of the binary Hamming scheme. We also give a representation theoretic characterization of this basis that explains its orthogonality, namely, that it is the canonically defined (up to scalars) symmetric Gelfand---Tsetlin basis.