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Goodwill and Other Intangibles (Tables) | 9 Months Ended
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Sep. 30, 2023
Goodwill and Other Intangibles |
Changes in the carrying amount of goodwill by segment | Changes in the carrying amount of goodwill for the nine months ended September 30, 2023, by segment, were as follows, in thousands: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | ​ | ​ |  | ​ |  | ​ | ​ | ​ | ​ |  | Accumulated |  | ​ | ​
​ | ​ | Gross Goodwill | ​ | ​ | ​ | FX Translation | ​ | Gross Goodwill | ​ | Impairment | ​ | Net Goodwill
​ | ​ | December 31, 2022 | ​ | Additions/Disposals | ​ | Adjustment | ​ | September 30, 2023 | ​ | Losses | ​ | September 30, 2023
Goodwill, by segment: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Installation | ​ | $ | 1,826,979 | ​ | $ | 72,998 | ​ | $ | - | ​ | $ | 1,899,977 | ​ | $ | (762,021) | ​ | $ | 1,137,956
Specialty Distribution | ​ |  | 902,036 | ​ |  | - | ​ | ​ | (215) | ​ |  | 901,821 | ​ |  | - | ​ |  | 901,821
Total goodwill | ​ | $ | 2,729,015 | ​ | $ | 72,998 | ​ | $ | (215) | ​ | $ | 2,801,798 | ​ | $ | (762,021) | ​ | $ | 2,039,777
Schedule of other intangible assets | Other intangible assets, net includes customer relationships, non-compete agreements, and trademarks / trade names. The following table sets forth our other intangible assets, in thousands: ​
​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | As of
​ |  | September 30, 2023 | ​ | December 31, 2022
Gross definite-lived intangible assets |  | $ | 825,552 | ​ | $ | 782,316
Accumulated amortization |  | ​ | (218,612) | ​ | ​ | (167,349)
Net definite-lived intangible assets |  | $ | 606,940 | ​ | $ | 614,967
Schedule of amortization expense | ​ The following table sets forth our amortization expense, in thousands: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Three Months Ended September 30, | ​ | Nine Months Ended September 30,
​ |  | 2023 |  | 2022 |  | 2023 |  | 2022
Amortization expense | ​ | $ | 17,389 | ​ | $ | 16,970 | ​ | $ | 51,496 | ​ | $ | 50,809
​

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