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pro vyhledávání: '"Madeline Locus"'
We show that the number of short binary signed-digit representations of an integer $n$ is equal to the $n$-th term in the Stern sequence. Various proofs are provided, including direct, bijective, and generating function proofs. We also show that this
Externí odkaz:
http://arxiv.org/abs/2308.07448
Which integers can be written as a quotient of sums of distinct powers of three? We outline our first steps toward an answer to this question, beginning with a necessary and almost sufficient condition. Then we discuss an algorithm that indicates whe
Externí odkaz:
http://arxiv.org/abs/2308.07252
Recently, Schneider and Schneider defined a new class of partitions called sequentially congruent partitions, in which each part is congruent to the next part modulo its index, and they proved two partition bijections involving these partitions. We i
Externí odkaz:
http://arxiv.org/abs/2208.04291
Publikováno v:
Australas. J. Combin. 82(2) (2022), 212--227
Partition theory abounds with bijections between different types of partitions. One of the most famous partition bijections maps each self-conjugate partition of a positive integer $n$ to a partition of $n$ into distinct odd parts, and vice versa. He
Externí odkaz:
http://arxiv.org/abs/2110.15837
Publikováno v:
Journal of Integer Sequences, Vol. 25 (2022), Article 22.5.1
Integer partitions express the different ways that a positive integer may be written as a sum of positive integers. Here we explore the analytic properties of a new polynomial $f_\lambda(x)$ that we call the partition polynomial for the partition $\l
Externí odkaz:
http://arxiv.org/abs/2108.00943
We study a bijective map from integer partitions to the prime factorizations of integers that we call the "supernorm" of a partition, in which the multiplicities of the parts of partitions are mapped to the multiplicities of prime factors of natural
Externí odkaz:
http://arxiv.org/abs/2107.14284
Publikováno v:
From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory. Operator Theory: Advances and Applications, Birkhauser (2021), 41-56
Hypergeometric functions over finite fields were introduced by Greene in the 1980s as a finite field analogue of classical hypergeometric series. These functions, and their generalizations, naturally lend themselves to, and have been widely used in,
Externí odkaz:
http://arxiv.org/abs/2101.06303
Publikováno v:
Res. Math. Sci. 8: 18 (2021)
Let $k \geq 2$ be an integer. Let $q$ be a prime power such that $q \equiv 1 \pmod {k}$ if $q$ is even, or, $q \equiv 1 \pmod {2k}$ if $q$ is odd. The generalized Paley graph of order $q$, $G_k(q)$, is the graph with vertex set $\mathbb{F}_q$ where $
Externí odkaz:
http://arxiv.org/abs/2006.14716
Akademický článek
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Publikováno v:
Arch. Math. 116 (2021), 487-500
In previous work, the authors confirmed the speculation of J. G. Thompson that certain multiquadratic fields are generated by specified character values of sufficiently large alternating groups $A_n$. Here we address the natural generalization of thi
Externí odkaz:
http://arxiv.org/abs/1912.07102