Exact prime-power block counts for isosceles MacMahon numbers
Year: 2026
Type: preprint
Abstract: For every prime p and integer e >= 1, we count exactly the positive parameter pairs 1 <= k,m < p^e for which the isosceles MacMahon number M(k,m,m) is not divisible by p. We obtain a closed expression for odd primes and the formula (e-1)2^(e-1) for p=2. The resulting counts give the growth order on general square blocks and zero two-dimensional density. Through the Li-Zanello criterion, they also enumerate weak Lefschetz parameters in the stated family of monomial complete intersections.
Author: Xu, Zihuan
Institution: Capital Normal University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223471489
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