Related papers: The triplication method for constructing strong st…
A novel approach to building strong starters in cyclic groups of orders $n$ divisible by 3 from starters of smaller orders is presented. A strong starter in $Z_n$ ($n$ odd) is a partition of the set $\{1,2,\dots,n-1\}$ into pairs…
In this paper we study some structure properties of primitive weird numbers in terms of their factorization. We give sufficient conditions to ensure that a positive integer is weird. Two algorithms for generating weird numbers having a…
A Sudoku puzzle often has a regular pattern in the arrangement of initial digits and it is typically made solvable with known solving techniques, called strategies. In this paper, we consider the problem of generating such Sudoku instances.…
We investigate all spherically symmetric fundamental monopole solutions with fixed topological charge in the SU(5) --> SU(3)xSU(2)xU(1)/Z_3xZ_2 symmetry breaking. We find that there is three-fold replication of the monopoles. The three…
Over the last decade, Sudoku, a combinatorial number-placement puzzle, has become a favorite pastimes of many all around the world. In this puzzle, the task is to complete a partially filled $9 \times 9$ square with numbers 1 through 9,…
Efficient arithmetic circuit design for resourceconstrained hardware involves challenging combinatorial optimization problems, among which Multiple Constant Multiplication (MCM) is a prominent example. MCM aims at implementing…
Strongly multiplicative linear secret sharing schemes (LSSS) have been a powerful tool for constructing secure multiparty computation protocols. However, it remains open whether or not there exist efficient constructions of strongly…
In 2000, Rees and Shalaby constructed simple indecomposable two-fold cyclic triple systems for all v congruent to 0, 1, 3, 4, 7, and 9 (mod 12) where v = 4 or v>11, using Skolem-type sequences. We construct, using Skolem-type sequences,…
Constructing active sets is a key part of the Multivariate Decomposition Method. An algorithm for constructing optimal or quasi-optimal active sets is proposed in the paper. By numerical experiments, it is shown that the new method can…
We give a possible explanation for the mystery of a missing number in the statement of a problem that asks for the non-negative integers to be partitioned into three subsets. We interpret the missing number as one of the clues that can lead…
Causal language modeling using the Transformer architecture has yielded remarkable capabilities in Large Language Models (LLMs) over the last few years. However, the extent to which fundamental search and reasoning capabilities emerged…
This paper investigates the problem of Secure Multi-party Batch Matrix Multiplication (SMBMM), where a user aims to compute the pairwise products…
The right triangles represented in the Plimpton 322 data have integer sides $(a, b, d)$ with $a < b < d$, by inspecting the data we propose $b=M\,Q_{M}$ with $M,Q_{M}$ positive integers. In this way we present a new data-driven family of…
The clustering problem has many applications in Machine Learning, Operations Research, and Statistics. We propose three algorithms to create starting solutions for improvement algorithms for this problem. We test the algorithms on 72…
We generalize staircase codes and tiled diagonal zipper codes, preserving their key properties while allowing each coded symbol to be protected by arbitrarily many component codewords rather than only two. This generalization which we term…
We present a typing system with non-idempotent intersection types, typing a term syntax covering three different calculi: the pure {\lambda}-calculus, the calculus with explicit substitutions {\lambda}S, and the calculus with explicit…
The tiling problem has been a famous problem that has appeared in many Mathematics problems. Many of its solutions are rooted in high-level Mathematics. Thus we hope to tackle this problem using more elementary Mathematics concepts. In this…
Despite their proficiency in various language tasks, Large Language Models (LLMs) struggle with combinatorial problems like Satisfiability, Traveling Salesman Problem, or even basic arithmetic. We address this gap through a novel trial &…
We develop analytical methods for computing the structure constant for three heavy operators, starting from the recently proposed hexagon approach. Such a structure constant is a semiclassical object, with the scale set by the inverse…
This paper deals with solving a class of three-by-three block saddle point problems. The systems are solved by preconditioning techniques. Based on an iterative method, we construct a block upper triangular preconditioner. The convergence…