TY - JOUR

T1 - On a restricted m-non-squashing partition function

AU - Rødseth, Oystein J.

AU - Sellers, James

PY - 2005/10/24

Y1 - 2005/10/24

N2 - For a fixed integer m ≥ 2, we say that a partition n = p1 + p2 + ⋯ + pk of a natural number n is m-non-squashing if p1 ≥ 1 and (m - 1)(p1 + ⋯ + Pj-i) ≤ pj for 2 ≤ j ≤ k. In this paper we give a, new bijective proof that the number of m-non-squashing partitions of n is equal to the number of m-ary partitions of n. Moreover, we prove a similar result for a certain restricted m-non-squashing partition function c(n) which is a natural generalization of the function which enumerates non-squashing partitions into distinct parts (originally introduced by Sloane and the second author). Finally, we prove that for each integer r ≥ 2, c(mr+1n) - c(mrn) = 0 (mod mr-1/dr-2), where d = gcd(2, m). partitions, m-non-squashing partitions, m-ary partitions, stacking boxes, congruences.

AB - For a fixed integer m ≥ 2, we say that a partition n = p1 + p2 + ⋯ + pk of a natural number n is m-non-squashing if p1 ≥ 1 and (m - 1)(p1 + ⋯ + Pj-i) ≤ pj for 2 ≤ j ≤ k. In this paper we give a, new bijective proof that the number of m-non-squashing partitions of n is equal to the number of m-ary partitions of n. Moreover, we prove a similar result for a certain restricted m-non-squashing partition function c(n) which is a natural generalization of the function which enumerates non-squashing partitions into distinct parts (originally introduced by Sloane and the second author). Finally, we prove that for each integer r ≥ 2, c(mr+1n) - c(mrn) = 0 (mod mr-1/dr-2), where d = gcd(2, m). partitions, m-non-squashing partitions, m-ary partitions, stacking boxes, congruences.

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M3 - Article

AN - SCOPUS:27644590201

SN - 1530-7638

VL - 8

JO - Journal of Integer Sequences

JF - Journal of Integer Sequences

IS - 5

ER -