Related papers: Chain Lemma, Quadratic Forms and Symbol Length
Tensor models are generalizations of matrix models, and are studied as discrete models of quantum gravity for arbitrary dimensions. Among them, the canonical tensor model (CTM for short) is a rank-three tensor model formulated as a totally…
Cyclic codes are an interesting type of linear codes and have applications in communication and storage systems due to their efficient encoding and decoding algorithms. They have been studied for decades and a lot of progress has been made.…
A word is level if each letter appears in it the same number of times, plus or minus 1. We give a complete characterization of the lengths for which level ternary circular square-free words exist. Key words: combinatorics on words, circular…
m-Qubit states are imbedded in $\mathfrak{Cl}_{2^m}$ Clifford algebras. Their probability spectra then depend on $O(2m)$ or $O(2m+1)$ invariants. Parameter domains for $O(2m(+1))-$ vector and tensor configurations, generalizing the notion…
Affine $\lambda$-terms are $\lambda$-terms in which each bound variable occurs at most once and linear $\lambda$-terms are $\lambda$-terms in which each bound variables occurs once. and only once. In this paper we count the number of closed…
In 1973, Calder\'{o}n proved that an $m \times 2$ positive semidefinite (psd) biquadratic form can always be expressed as the sum of ${3m(m+1) \over 2}$ squares of quadratic forms. Very recently, by applying Hilbert's theorem on ternary…
In this paper, study sums $A=\{a,b\}_2+\{c,d\}_2$ of two symbols in $K_2(F)/2K_2(F)$ when $\operatorname{char}(F)=2$. We first prove a chain lemma that connects $A$ to $B=\{\alpha,\beta\}_2+\{\gamma,\delta\}_2$ by a finite sequence of small…
BCH codes are an important class of cyclic codes, and have wide applicantions in communication and storage systems. However, it is difficult to determine the parameters of BCH codes and only a few cases are known. In this paper, we mainly…
We give the symmetric version of five lemmas which are essential for the theory of tensor products (and norms). These are: the approximation, extension, embedding, density and local technique lemmas. Some application of these tools to the…
We construct explicitly in any finite field of the form Fq[x]/(x^m-a) elements with multiplicative order at least 2^{(2m)^(1/2)}
In this paper we consider the following problems: how many different subsets of Sigma^n can occur as set of all length-n factors of a finite word? If a subset is representable, how long a word do we need to represent it? How many such…
John Tromp introduced the so-called 'binary lambda calculus' as a way to encode lambda terms in terms of binary words. Later, Grygiel and Lescanne conjectured that the number of binary lambda terms with $m$ free indices and of size $n$…
We give bounds on the L(2,1)-labeling number of a simple graph in terms of its order and its maximum degree. We also describe an infinite class of graphs of which the elements have the highest L(2,1)-labeling numbers in terms of their…
We give universal upper bounds on the relative dimensions of isotypic components of a tensor product of the linear group GL(n) representations and universal upper bounds on the relative dimensions of irreducible components of a tensor…
If $x$ is a non-empty string then the repetition $xx$ is called a tandem repeat. Similarly, a tandem in a two dimensional array $X$ is a configuration consisting of a same primitive block $W$ that touch each other with one side or corner.…
We functorially identify similarity classes of line-bundle-valued quadratic forms on rank two vector bundles with isomorphism classes of pairs consisting of the degree zero and the degree one parts of the associated generalized Clifford…
QCD sum rules for the determination of form factors of $\Lambda_b$ and $\Lambda_c$ semileptonic decays are investigated. With a form for the baryonic current appropriate for the limits of the heavy quark symmetries, the different tensor…
In the paper an explicit formula for an arbitrary $6j$-symbol for finite-dimensional irreducible representations of the algebra $\mathfrak{gl}_3$ is derived. A $6j$-symbol is written as a result of substitution of $\pm 1$ into a series of…
We study the iterated limit of a quaternary of means of four terms through the period map from the family of cyclic fourfold coverings of the complex projective line branching at six points to the three-dimensional complex ball…
We consider cyclic codes $\mathcal{C}_\mathcal{L}$ associated to quadratic trace forms in $m$ variables $Q_R(x) = \operatorname{Tr}_{q^m/q}(xR(x))$ determined by a family $\mathcal{L}$ of $q$-linearized polynomials $R$ over…