On partitions with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e506" altimg="si6.svg"><mml:mi>k</mml:mi></mml:math> corners not containing the staircase with one more corner
نویسندگان
چکیده
We give three proofs of the following result conjectured by Carriegos, De Castro-Garc\'{\i}a and Mu\~noz Casta\~neda in their work on enumeration control systems: when $\binom{k+1}{2} \le n < \binom{k+2}{2}$, there are as many partitions $n$ with $k$ corners pairs $(\alpha, \beta)$ such that + |\alpha| |\beta| = n$.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2022
ISSN: ['1872-6771', '0166-218X']
DOI: https://doi.org/10.1016/j.dam.2022.02.012