Combinatorics of triangular partitions
نویسندگان
چکیده
منابع مشابه
Combinatorics of Integer Partitions in Arithmetic Progression
The partitions of a positive integer n in which the parts are in arithmetic progression possess interesting combinatorial properties that distinguish them from other classes of partitions. We exhibit the properties by analyzing partitions with respect to a fixed length of the arithmetic progressions. We also address an open question concerning the number of integers k for which there is a k-par...
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A celebrated result of Gauss states that every positive integer can be represented as the sum of three triangular numbers. In this article we study p3∆(n), the number of partitions of the integer n into three triangular numbers, as well as p3∆(n), the number of partitions of n into three distinct triangular numbers. Unlike t(n), which counts the number of representations of n into three triangu...
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We study oscillations in the eigenfunctions for a fractional Schrödinger operator on the real line. An argument in the spirit of Courant’s nodal domain theorem applies to an associated local problem in the upper half plane and provides a bound on the number of nodal domains for the extensions of the eigenfunctions. Using the combinatorial properties of noncrossing partitions, we turn the nodal ...
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We examine the combinatorial significance of Ramanujan’s famous summation. In particular, we prove bijectively a partition theoretic identity which implies the summation formula.
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ژورنال
عنوان ژورنال: Enumerative combinatorics and applications
سال: 2022
ISSN: ['2710-2335']
DOI: https://doi.org/10.54550/eca2023v3s1r1