Séminaire Lotharingien de Combinatoire, 95B.38 (2026), 12 pp.
Ivan Balashov, Constantine Bulavenko and Yaroslav Molybog
Asymptotics of Generalized Tesler Matrices
Abstract.
This paper studies the asymptotic enumeration of generalized Tesler matrices. To suit this goal, we introduce integral Tesler matrices, linking Tesler matrices to integer partitions and obtaining sharp logarithmic asymptotics for flat hook sum vectors.
We then introduce height diagrams to decompose more complicated hook sum vectors into flat pieces. Thereby, we establish the asymptotics of Tesler matrices with staircase hook sum vectors, significantly improving the best known bounds. In particular, the logarithmic asymptotic for the number of regular Tesler matrices is obtained.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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