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Shareholders' equity
 9 Months Ended
Sep. 30, 2022
Equity [Abstract]  
Long-term incentive compensation Shareholders' equity
Stock-based compensation
During the nine months ended September 30, 2022, the Company granted 1,129 restricted and performance stock units with an aggregate grant-date fair value of $122,356 and a weighted-average expected life of approximately 3.5 years and 130 stock-settled stock appreciation rights with an aggregate grant-date fair value of $4,573 and a weighted-average expected life of approximately 4.5 years.
As of September 30, 2022, the Company had $182,083 in total estimated but unrecognized stock-based compensation expense under the Company's equity compensation and employee stock purchase plans. The Company expects to recognize this expense over a weighted average remaining period of 1.3 years.
Share repurchases
Share repurchases
The following table summarizes the Company's common stock repurchases during the three and nine months ended September 30, 2022 and 2021:
Three months ended September 30,Nine months ended September 30,
2022202120222021
Open market repurchases:
Shares repurchased2,122 2,731 8,095 7,750 
Amount paid$184,797 $336,217 $787,854 $899,447 
Average paid per share$87.10 $123.14 $97.33 $116.06 
The Company did not repurchase any shares subsequent to September 30, 2022 through October 27, 2022.
The Company is authorized to make purchases from time to time in the open market or in privately negotiated transactions, including without limitation, through accelerated share repurchase transactions, derivative transactions, tender offers, Rule 10b5-1 plans or any combination of the foregoing, depending upon market conditions and other considerations.
As of October 27, 2022, the Company had a total of $1,596,085 available under the current authorization for additional share repurchases. Although this share repurchase authorization does not have an expiration date, the Company remains subject to share repurchase limitations including under the terms of its current senior secured credit facilities.