scholarly journals Motzkin numbers and related sequences modulo powers of 2

2018 ◽  
Vol 73 ◽  
pp. 114-137
Author(s):  
C. Krattenthaler ◽  
T.W. Müller
Keyword(s):  
Motzkin Numbers ◽  
Powers Of 2

scholarly journals Associative spectra of graph algebras I

2021 ◽  
Author(s):  
Erkko Lehtonen ◽  
Tamás Waldhauser
Keyword(s):  
Catalan Numbers ◽  
Graph Algebras ◽  
Undirected Graphs ◽  
Powers Of 2

AbstractAssociative spectra of graph algebras are examined with the help of homomorphisms of DFS trees. Undirected graphs are classified according to the associative spectra of their graph algebras; there are only three distinct possibilities: constant 1, powers of 2, and Catalan numbers. Associative and antiassociative digraphs are described, and associative spectra are determined for certain families of digraphs, such as paths, cycles, and graphs on two vertices.

scholarly journals Bijections and Congruences for Generalizations of Partition Identities of Euler and Guy

10.37236/1796 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
James A. Sellers ◽  
Andrew V. Sills ◽  
Gary L. Mullen
Keyword(s):  
Famous Theorem ◽  
Partition Identities ◽  
Product Identity ◽  
Powers Of 2 ◽  
Pentagonal Number Theorem ◽  
Series Product

In 1958, Richard Guy proved that the number of partitions of $n$ into odd parts greater than one equals the number of partitions of $n$ into distinct parts with no powers of 2 allowed, which is closely related to Euler's famous theorem that the number of partitions of $n$ into odd parts equals the number of partitions of $n$ into distinct parts. We consider extensions of Guy's result, which naturally lead to a new algorithm for producing bijections between various equivalent partition ideals of order 1, as well as to two new infinite families of parity results which follow from Euler's Pentagonal Number Theorem and a well-known series-product identity of Jacobi.

scholarly journals HECKE-TYPE CONGRUENCES FOR ANDREWS' SPT-FUNCTION MODULO 16 AND 32

2014 ◽  
Vol 10 (02) ◽  
pp. 375-390 ◽  
Author(s):  
FRANK G. GARVAN ◽  
CHRIS JENNINGS-SHAFFER
Keyword(s):  
Generating Function ◽  
Hecke Operators ◽  
Powers Of 2

Inspired by recent congruences by Andersen with varying powers of 2 in the modulus for partition related functions, we extend the modulo 32760 congruences of the first author for the function spt (n). We show that a normalized form of the generating function of spt (n) is an eigenform modulo 32 for the Hecke operators T(ℓ2) for primes ℓ ≥ 5 with ℓ ≡ 1, 11, 17, 19 (mod 24), and an eigenform modulo 16 for ℓ ≡ 13, 23 (mod 24).

Two prime squares, four prime cubes and powers of 2

2019 ◽  
Vol 187 (2) ◽  
pp. 143-150
Author(s):  
Xiaodong Zhao
Keyword(s):  
Powers Of 2 ◽  
Prime Squares

On a Problem of P. Erdös

1972 ◽  
Vol 15 (2) ◽  
pp. 309-310 ◽  
Author(s):  
I. Ruzsa
Keyword(s):  
Absolute Constant ◽  
Infinite Sequence ◽  
Affirmative Answer ◽  
Powers Of 2 ◽  
Image Position

P. Erdös asked the following problem: Does there exist an infinite sequence of integers a1<…satisfying for every x≥11so that every integer is of the form 2k+ai [1]. The analogous questions can easily be answered affirmatively if the powers of 2 are replaced by the rth power.In this note we give a simple affirmative answer to the problem of Erdôs. Let c2 be a sufficiently small absolute constant. Our sequence A consists of all the integers of the form2

SOME REMARKS ON MINIMAL ASYMPTOTIC BASES OF ORDER THREE

2020 ◽  
Vol 102 (1) ◽  
pp. 21-30
Author(s):  
DENGRONG LING ◽  
MIN TANG
Keyword(s):  
Acta Arith ◽  
Powers Of 2

We study a question on minimal asymptotic bases asked by Nathanson [‘Minimal bases and powers of 2’, Acta Arith. 49 (1988), 525–532].

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