Related papers: Olry Terquem's forgotten problem
A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of…
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…
Sorting is one of the most used and well investigated algorithmic problem [1]. Traditional postulation supposes the sorting data archived, and the elementary operation as comparisons of two numbers. In a view of appearance of new processors…
A recursive algorithm is constructed which finds all solutions to a class of Diophantine equations connected to the problem of determining ordered n-tuples of positive integers satisfying the property that their sum is equal to their…
This paper is a supplement to a talk for mathematics teachers given at the 2016 LSU Mathematics Contest for High School Students. The paper covers more details and aspects than could be covered in the talk. We start with an interesting…
Tight bounds on the block entropy of patterns of sequences generated by independent and identically distributed (i.i.d.) sources are derived. A pattern of a sequence is a sequence of integer indices with each index representing the order of…
The palindrome pattern matching (pal-matching) is a kind of generalized pattern matching, in which two strings $x$ and $y$ of same length are considered to match (pal-match) if they have the same palindromic structures, i.e., for any…
In-place associative integer sorting technique was proposed for integer lists which requires only constant amount of additional memory replacing bucket sort, distribution counting sort and address calculation sort family of algorithms.…
The topic of this paper is the distributed and incremental generation of long executions of concurrent systems, uniformly or more generally with weights associated to elementary actions. Synchronizing sequences of letters on alphabets…
Given natural numbers $n$ and $k$, with $n>k$, the Prouhet-Tarry-Escott (PTE) problem asks for distinct subsets of $\Z$, say $X=\{x_1,...,x_n\}$ and $Y=\{y_1,...,y_n\}$, such that \[x_1^i+...+x_n^i=y_1^i+...+y_n^i\] for $i=1,...,k$. Many…
Tewodros Amdeberhan and Armin Straub initiated the study of enumerating subfamilies of the set of (s,t)-core partitions. While the enumeration of (n+1,n+2)-core partitions into distinct parts is relatively easy (in fact it equals the…
A cryptarithm (or alphametic) is a mathematical puzzle in which numbers are represented with words in such a way that identical letters stand for equal digits and distinct letters for unequal digits. An alphametic puzzle is usually given in…
We study growth rates of generalised Fibonacci sequences of a particular structure. These sequences are constructed from choosing two real numbers for the first two terms and always having the next term be either the sum or the difference…
The problem to compute the vertices of a polytope given by affine inequalities is called vertex enumeration. The inverse problem, which is equivalent by polarity, is called the convex hull problem. We introduce `approximate vertex…
Let $A$ and $B$ be two number sequences of length $n$ and $m$, respectively, where $m\le n$. Given a positive number $\delta$, a common almost increasing sequence $s_1\ldots s_k$ is a common subsequence for both $A$ and $B$ such that for…
In-place associative integer sorting technique was developed, improved and specialized for distinct integers. The technique is suitable for integer sorting. Hence, given a list S of n integers S[0...n-1], the technique sorts the integers in…
We consider the problem of sequencing a set of positive numbers. We try to find the optimal sequence to maximize the variance of its partial sums. The optimal sequence is shown to have a beautiful structure. It is interesting to note that…
Problems on repeated geometric patterns in finite point sets in Euclidean space are extensively studied in the literature of combinatorial and computational geometry. Such problems trace their inspiration to Erd\H{o}s' original work on that…
Hofstadter's Q-sequence remains an enigma fifty years after its introduction. Initially, the terms of the sequence increase monotonically by 0 or 1 at a time. But, Q(12)=8 while Q(11)=6, and monotonicity fails shortly thereafter. In this…
We consider a sequence of independent random variables with the known distribution observed sequentially. The observation $n$ is assumed to be a value of one order statistics such as s:n-th, where 1 is less than s is less than n. It the…