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# On congruence schemes for constant terms and their applications

On congruence schemes for constant terms and their applications
Armin Straub — Research in Number Theory — Volume 8, Number 3, 2022, Pages 1-21, #42

## Sage package

This paper is accompanied by a Sage package that implements the computation of congruence schemes for constant terms.

## Abstract

Rowland and Zeilberger devised an approach to algorithmically determine the modulo $$p^r$$ reductions of values of combinatorial sequences representable as constant terms (building on work of Rowland and Yassawi). The resulting $$p$$-schemes are systems of recurrences and, depending on their shape, are classified as automatic or linear. We revisit this approach, provide some additional details such as bounding the number of states, and suggest a third natural type of scheme that combines benefits of automatic and linear ones. We illustrate the utility of these "scaling" schemes by confirming and extending a conjecture of Rowland and Yassawi on Motzkin numbers.

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## BibTeX

@article{congruenceschemes-ct-2022,
author = {Armin Straub},
title = {On congruence schemes for constant terms and their applications},
journal = {Research in Number Theory},
year = {2022},
volume = {8},
number = {3},
pages = {1--21, #42},
doi = {10.1007/s40993-022-00337-6},
}