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For any finite totally ordered set, the multisets of intervals form an abelian category. Various classes of subcategories admit natural combinatorial descriptions, and counting them yields familiar integer sequences. Surprisingly, in some…
We simplify construction of Thoma representations of an infinite symmetric group
In this paper, we consider representations of integers as sums of at most four distinct $m$-gonal numbers (allowing a fixed number of repeats of each polygonal number occurring in the sum). We show that the number of such representations…
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…
A generating function for reciprocal binomial coefficients is written down, integral representations of this function are obtained, generating functions for sums of reciprocal binomial coefficients are derived, new identities are obtained,…
We investigate how to model exchangeability with choice functions. Exchangeability is a structural assessment on a sequence of uncertain variables. We show how such assessments are a special indifference assessment, and how that leads to a…
For a set of nonnegative integers $S$ let $R_{S}(n)$ denote the number of unordered representations of the integer $n$ as the sum of two different terms from $S$. In this paper we focus on partitions of the natural numbers into two sets…
We identify a partition-theoretic generalization of Riemann zeta function and the equally positive integer-indexed harmonic sums at infinity, to obtain the generating function and the integral representations of the latter. The special…
We present a construction that gives an infinite series of divisible design graphs which are Cayley graphs.
The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to…
In a recent paper, two multi-representations for the measurable sets in a computable measure space have been introduced, which prove to be topologically complete w.r.t. certain topological properties. In this contribution, we show them…
In this paper, we obtain formulas for the number of representations of positive integers as sums of arbitrarily many squares (and other polygonal numbers) with a certain natural weighting. The resulting weighted sums give Fourier…
Finite and Infinite-dimensional representations of symmetry algebras play a significant role in determining the spectral properties of physical Hamiltonians. In this paper, we introduce and apply a practical method to construct infinite…
Multisets are sets that allow repetition of elements. As such, multisets pave the way to a number of interesting possibilities of theoretical and applied nature. In the present work, after revising the main aspects of traditional sets, we…
Many mathematical statements have the following form. If something is true for all finite subsets of an infinite set $I$, then it is true for all of $I$. This paper describes some old and new results on infinite sets of linear and…
In contrast to finite arithmetic configurations, relatively little is known about which infinite patterns can be found in every set of natural numbers with positive density. Building on recent advances showing infinite sumsets can be found,…
Four constructions result from a desire to create enhancements to Cantor's infinite real set cardinality. Each continues to keep Cantor's cardinality formulation in place while providing new comparisons of arbitrary infinite sets. To…
Several structural properties of a universal algebra can be seen from the higher commutators of its congruences. Even on a finite algebra, the sequence of higher commutator operations is an infinite object. In the present paper, we exhibit…
We study the representability of sets that admit extended formulations using mixed-integer bilevel programs. We show that feasible regions modeled by continuous bilevel constraints (with no integer variables), complementarity constraints,…
The problem of representation of elements of weighted space of infinitely differentiable functions on real line by exponential series is considered.