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We construct infinitely many signed graphs having symmetric spectrum, by using the NEPS and rooted product of signed graphs. We also present a method for constructing large cospectral signed graphs. Although the obtained family contains…
The Hermitian, complex and fermionic two-matrix models with infinite set of variables are constructed. We show that these two-matrix models can be realized by the $W$-representations. In terms of the $W$-representations, we derive the…
Several combinatorial identities are presented, involving Stirling functions of the second kind with a complex variable. The identities involve also Stirling numbers of the first kind, binomial coefficients and harmonic numbers.
We define integer multimodal sequences, which are generalizations of unimodal sequences having multiple local peaks of equal size. The generating functions for multimodal sequences represent novel types of $q$-series that combine generating…
We consider complete intersection ideals in a polynomial ring over a field of characteristic zero that are stable under the action of the symmetric group permuting the variables. We determine the possible representation types for these…
This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…
In this note, we introduce a new kind of pair of finite range sets in $\mathbb{C}$ for meromorphic functions corresponding to their uniqueness, i.e., how two meromorphic functions are uniquely determined by their two finite shared sets.
We study the modular representation theory of the symmetric and alternating groups. One of the most natural ways to label the irreducible representations of a given group or algebra in the modular case is to show the unitriangularity of the…
We give a simple and efficient process for generating a quantum superposition of states which form a discrete approximation of any efficiently integrable (such as log concave) probability density functions.
Difference triangle sets are useful in many practical problems of information transmission. This correspondence studies combinatorial and computational constructions for difference triangle sets having small scopes. Our algorithms have been…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
Multiple binomial sums form a large class of multi-indexed sequences, closed under partial summation, which contains most of the sequences obtained by multiple summation of products of binomial coefficients and also all the sequences with…
In this paper, we consider representations of integers as sums of generalized heptagonal numbers with a prescribed number of repeats of each heptagonal number appearing in the sum. In particular, we investigate the classification of such…
This paper presents a novel set-based computing method, called interval superposition arithmetic, for enclosing the image set of multivariate factorable functions on a given domain. In order to construct such enclosures, the proposed…
We present and study new definitions of universal and programmable universal unary functions and consider a new simplicity criterion: almost decidability of the halting set. A set of positive integers S is almost decidable if there exists a…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric integer programs are studied from a group theoretical viewpoint. We investigate the structure of integer solutions of integer programs and show…
This paper contains a complete description of classes of the unitary equivalence of the admissible representations of infinite-dimensional classic matrix groups paper.
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…
We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.
We study the representation dimension of the class of algebras known as quantum complete intersections. For such an algebra, we show that the representation dimension is at most twice its codimension. Moreover, we show that the…