相关论文: Combinatorial identities for binary necklaces from…
We introduce several new constructions for perfect periodic autocorrelation sequences and arrays over the unit quaternions. This paper uses both mathematical proofs and com- puter experiments to prove the (bounded) array constructions have…
We study several kinds of polynomial ensembles of derivative type which we propose to call P\'olya ensembles. These ensembles are defined on the spaces of complex square, complex rectangular, Hermitian, Hermitian anti-symmetric and…
In combinatorics, P\'{o}lya's Enumeration Theorem is a powerful tool for solving a wide range of counting problems, including the enumeration of groups, graphs, and chemical compounds. In this paper, we present an extension of P\'{o}lya's…
Rotational spectroscopy is the most accurate method for determining structures of molecules in the gas phase. It is often assumed that a rotational spectrum is a unique "fingerprint" of a molecule. The availability of large molecular…
We present a novel framework for deriving on-shell recursion relations, with a specific focus on biadjoint and pure Yang-Mills theories. Starting from the double-cover CHY factorization formulae, we identify a suitable set of independent…
In this article we give explicit descriptions of the multiplicities of some classes of monomial ideals. For instance, we give a formula for the multiplicities of all codimension 1 monomial ideals, and another formula for the multiplicities…
Large surveys producing tera- and petabyte-scale databases require machine-learning and knowledge discovery methods to deal with the overwhelming quantity of data and the difficulties of extracting concise, meaningful information with…
We present the results of time-resolved spectroscopy of 13 O-type stars in the Cas OB6 stellar association. We conducted a survey for radial velocity variability in search of binary systems, which are expected to be plentiful in young OB…
Detached eclipsing double line spectroscopic binaries offer an opportunity to measure directly stellar parameters: mass, luminosity, radius, as well as the distance. The only non-trivial step is the need to determine surface brightness of…
We show that there is a very simple approach to determine the 2-adic complexity of periodic binary sequences with ideal two-level autocorrelation. This is the first main result by H. Xiong, L. Qu, and C. Li, IEEE Transactions on Information…
In a simple abelian spinor field theory, the canonical trace identities for certain axial-vector and axial-scalar operators are reexamined in dimensional regularization, some disagreements with previous results are found and an interesting…
A grid class consists of permutations whose pictorial depiction can be partitioned into increasing and decreasing parts as determined by a given matrix. In this paper, we introduce a method for enumerating cyclic permutations in vector grid…
In this article, we present a concise combinatorial formula for efficiently determining the Wedderburn decomposition of rational group algebra associated with a split metacyclic $p$-group $G$, where $p$ is an odd prime. We also provide a…
Han recently discovered new hook length identities for binary trees. In this paper, we extend Han's identities to binomial families of trees. Moreover, we present a bijective proof of one of the identities for the family of ordered trees.
In this paper, a recent method to construct complementary sequence sets and complete complementary codes by Hadamard matrices is deeply studied. By taking the algebraic structure of Hadamard matrices into consideration, our main result…
We study cluster algebra of affine type $A_1^{(1)}$ by using two methods including counting the numbers of perfect matchings on snake graphs and compatible pairs on maximal Dyck paths. We find that the sum of coefficients of the terms in…
The pairing hierarchy of perfect pairing (PP), perfect quadruples (PQ) and perfect hextuples (PH) are sparsified coupled cluster models that are exact in a pairing active space for 2, 4, and 6 electron clusters, respectively. We describe…
Ulam words are binary words defined recursively as follows: the length-$1$ Ulam words are $0$ and $1$, and a binary word of length $n$ is Ulam if and only if it is expressible uniquely as a concatenation of two shorter, distinct Ulam words.…
This article discusses some difficulties in the implementation of combinatorial algorithms associated with the choice of all elements with certain properties among the elements of a set with great cardinality.The problem has been resolved…
In this paper, we present a general framework for the derivation of interesting finite combinatorial sums starting with certain classes of polynomial identities. The sums that can be derived involve products of binomial coefficients and…